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Issue N. 14 - 2018 ARGO New Frontiers in Practical Risk Management
Issue N. 14 - 2018
ARGONew Frontiers in Practical Risk Management
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Argo Magazine
Iason Consulting ltd is the editor and the publisher of Argo magazine. Neither editor is responsiblefor any consequence directly or indirectly stemming from the use of any kind of adoption of themethods, models, and ideas appearing in the contributions contained in this magazine, nor theyassume any responsibility related to the appropriateness and/or truth of numbers, figures, andstatements expressed by authors of those contributions.
Argo magazine
Year 2018 - Issue Number 14Published in October 2018First published in October 2013
Last published issues are available online:http://www.iasonltd.com/research
Front Cover: Lorenzo Raffo, After, 2018.
Copyright c�2018Iason Consulting ltd. All rights reserved.
New Frontiers in Pratical Risk Management
Editors:Antonio CASTAGNA (Managing Partner and CEO of Iason Consulting ltd)Luca OLIVO (Managing Director Iason Italia)
Executive Editor:Giulia PERFETTI
Graphic Designer:Lorena CORNA
Scientific Editorial Board:Gianbattista ARESIAntonio CASTAGNADario ESPOSITOMassimo GUARNIERILuca OLIVOMassimiliano ZANONI
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Contact Information:[email protected]
Iason Consulting ltd is registered trademark.
Articles submission guidelinesArgo welcomes the submission of articles on topical subjects related to the risk management.The six core sections are ALM & IRRBB, Credit, Trading book, Stress Test, AdvancedTechnology and New Market Standards. Within these six macro areas, articles can beindicatively, but not exhaustively, related to models and methodologies for market, credit,liquidity risk management, valuation of derivatives, asset management, trading strategies,statistical analysis of market data and technology in the financial industry. All articles shouldcontain references to previous literature. The primary criteria for publishing a paper are itsquality and importance to the field of finance, without undue regard to its technical difficulty.Argo is a single blind refereed magazine: articles are sent with author details to the ScientificCommittee for peer review. The first editorial decision is rendered at the latest within 60 daysafter receipt of the submission. The author(s) may be requested to revise the article. The editorsdecide to reject or accept the submitted article. Submissions should be sent to the technicalteam ([email protected]). LATEX or Word are the preferred format, but PDFs are accepted ifsubmitted with LATEX code or a Word file of the text. There is no maximum limit, butrecommended length is about 4,000 words. If needed, for editing considerations, the technicalteam may ask the author(s) to cut the article.
Copyright c�2018Iason Consulting ltd. All rights reserved.
Argo Magazine
Issue n. 14 / 20183
New Frontiers in Pratical Risk Management
Table of Contents
Editorial p. 5
New Market Standards
Interest Rate Benchmarks Reform:Time to Transition is NowRaphael Cavallari and Luca Olivo
About the Authors p. 7Introduction p. 9Main Steps of the Reform p. 10Business Implications p. 11Technical Implications p. 13Conclusions p. 15References p. 17
An overview of BREXIT effects onthe Banking SystemElia Stucchi
About the Authors p. 19Introduction p. 20Who? Actors Involved p. 20What? The BREXIT Effects p. 22Conclusions p. 25References p. 26
Banking Book
Analysis of the New Standards toMeasure and Manage the InterestRate Risk of the Banking BookIssued By BIS CommitteeAntonio Castagna
About the Authors p. 28Introduction p. 29Definition of the Interest Rate Risk of theBanking Book p. 29The IRRBB Framework p. 35Measuring the IRRBB Risk p. 38The Standardised Framework p. 53Conclusions p. 60References p. 61
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Editorial
Dear Readers,
This Argo Issue celebrates 5 years of the magazine, firstly published inOctober 2013. It is a great goal achieved thanks to the precious work of all thepeople that have contributed to the magazine realization during these years.Thanks to All!
This issue is mainly focused on two important events that will affect banks’activities during the next year: the transition to new Risk-Free Rates benchmarksand the Brexit. To this purpose, we have created a dedicated section called “NewMarket Standards".
We open this section with a qualitative contribute about the oncoming reformingprocess of Interest Rate Benchmarks: “Interest Rate Benchmarks Reform: Time toTransition is Now”. The authors, Raphael Cavallari and Luca Olivo, provide ageneral overview on the reform, pointing out its potential implications on bothbusiness and technical aspects of the banking processes, with focus on the RiskManagement fields.
Following in the section, you will read a brief article on the effects of BREXIT; in“An overview of BREXIT effects on the Banking System" Elia Stucchi presentsa review of the systemic effects for the banks active in the Community marketand in the UK, focusing also on the possible developments that banks will face tomitigate the risks inherent to this event.
Finally, within the Banking Book section we propose Antonio Castagna’s con-tribution “Analysis of the New Standards to Measure and Manage the InterestRate Risk of the Banking Book Issued By BIS Committee”; the article, alreadypublished in March 2018, presents an analysis of the new standards issued inApril 2016 by Basel Committee, on the measurement and the managements of theIRRBB.
We conclude, as usual by encouraging the submission of contributions for the nextissue of Argo to help improve and innovate this newsletter every time. Detailedinformation on how to contribute is on the front pages.
Enjoy your reading!
Antonio CastagnaLuca Olivo
Giulia Perfetti
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New MarketStandards
Interest Rate Benchmarks Reform:Time to Transition is Now
Argo Magazine
About the Authors
Raphael CavallariFinancial EngineerHe graduates in Theoretical Physics at theUniversity of Padua with a thesis written dur-ing an Exchange Programm at the ImperialCollege London. In 2017 he is awarded byIason being the best company candidate forthe Executive Master in Quantitative Financeat MIP Politecnico di Milano. As FinancialEngineer currently he is working in a highlyqualified Iason team that supports the RiskManagement Department of a major ItalianBank. He mainly deals with Risk ModelsGovernance activities concerning Equity andCommodity derivative instruments.
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New Market Standards
About the Authors
Luca OlivoManaging DirectorAfter the MSc in Finance at Bocconi Univer-sity in Milan, he starts as Business Analystin Iason Consulting, being involved in a chal-lenging project regarding the validation of theCCR internal model of a big pan-Europeanbank. As Functional Leader within the com-pany he follows several projects of Front-to-Risk integrations, moving from Milan to Lon-don, Munich and Vienna. From 2015 he leadsas Project Manager a highly qualified Iasonteam in order to support a big pan-Europeanbank in the implementation of new productsand market standards within its Risk frame-work; the team is also responsible for themonitoring of the main financial risk metricsrelated to new products and standards imple-mentation. From 2015 to 2017 the team is ableto fully deliver more than 100 implementa-tion projects for its client. Starting from 2017he contributes to create a new Iason team inorder to support another Systemically Impor-tant Financial Institution in the Risk ModelsGovernance and during the periodical on-siteinspections of ECB for the review of the inter-nal models.From May 2017 he is the Managing Directorof Iason Italia.
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Interest Rate Benchmarks Reform:Time to Transition is Now
aaaa
Raphael Cavallari Luca Olivo
T he paper provides a general overview on the ongoing process of reforming Interest Rate Benchmarks,with particular attention to the Euro Area. The authors highlight the potential implications that thisreform would have on both business and technical aspects of banks’ processes, with focus on the Risk
Management fields. Due to the magnitudo of the change and the challenges posed by its implications, theauthors believe banks should start transition processes now in order to minimize disruption when current IRbenchmarks will cease to be contributed (for some of them as early as 2020). In addition, they suggest bankscould take this transition also as a chance to optimize current processes within their risk frameworks in orderto reduce complexity and increase efficiency.
The need of reforming Interest Rates (IR)benchmarks mainly derives from theproblem emerged during the last global
financial crisis, when the first allegations of ma-nipulations and general misconduct in the de-termination of various Inter-Bank Offer Rates(IBORs) came to light. After findings againstvarious financial institutions became official, thefirst aim of the regulatory and supervisory bod-ies was to restore the confidence in IBORs world-wide. An extensive preliminary work done byregulatory agents resulted in the publicationof the “Principles for Financial Benchmarks: FinalReport” by the International Organization of Se-curities Commissions (IOSCO)[1]. This reportfocuses on four main aspects of a benchmarkdetermination:
1. Governance
2. Quality of Benchmark
3. Quality of the Methodology
4. Accountability
However, in our view, the core of IOSCOprinciples can be summarised in the prescrip-tion that a risk-free rate benchmark has to be de-termined from or be anchored to - wherever fea-sible - real and sound transactions1 being per-
formed at arm’s length in a well behaved mar-ket (in terms of size, liquidity, concentration).Moreover, the determination should also be sup-ported by a flexible and transparent methodol-ogy. This solution is fundamental in order for abenchmark:
• to be free of conflicts of interest;
• to be an accurate and reliable representa-tion of the economic realities of the inter-est it seeks to measure.
Here comes the main sticking point: inthe last decades the money market has expe-rienced substantial changes. As described inthe “Pre-Live Verification Program, Outcome andWay Forward” by the European Money MarketsInstitutes (EMMI)[8]:
[. . . ] The current regulatory environment andmonetary policy, including negative interest rates,and other sources of liquidity available to marketparticipants (which has reduced the need for financialinstitutions to obtain market-based funding), arefactors that have led to such changes in the activityin the unsecured money market. [. . . ]
The most visible change from the variousstatistical analyses performed by several mone-tary institutions (ECB, EMMI, FCA and IBA) is
1via competitive forces of supply and demand.
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that the money market moved from being prin-cipally interbank-based to a broader wholesalemarket, where transactions with other financialcorporations represent a sizable portion of theunsecured borrowing. Other market changesare a predominance of data availability forunsecured borrowing transactions (instead oflending) and the concentration of unsecuredtransactions in the very-short term maturities.All these market changes made all the reformsaimed to restore the confidence in the relevantbenchmark rates (e.g. EONIA and IBORs) notsufficient to keeping them alive in the long term.
Indeed, although the governance and pro-cess improvements were actually successful, theconditions of relevant markets changed in sucha manner that the representativeness of the in-dexes could not be restored.
This situation has also been exacerbated bythe new European Benchmark Regulation[6](EU BMR), which translates in a European reg-ulation the Principles stated in the IOSCO re-port. In particular, Article 11(1.a) of the EUBRM states that “the input data shall be sufficientto represent accurately and reliably the market oreconomic reality that the benchmark is intended tomeasure”. Moreover, under Article 51 of thesame regulation, “an index provider providing abenchmark on 30 June 2016 shall apply for authori-sation or registration and may continue to provideit until 1 January 2020 or unless such authorisationis refused”. In particular, even if the relevantcompetent authority could permit the use of thebenchmark in order not to frustrate or breachthe terms of financial contracts or instruments,no financial instruments shall add a referenceto such an existing benchmark after 1 January2020. The deadline of 2020 for the continuationof a benchmark is going to have far reachingconsequences among financial institutions andbeyond.
Given this background, with this article wewould like to provide a qualitative analysis onthe implications and challenges that the finan-cial institutions could face in benchmarks tran-sition, with a particular focus on the Euro Area.In the next section we outline the most relevantsteps in the reform, while the second sectionis dedicated to general implications in banks’business activities. The third section is focusedon technical implications by a risk managementpoint of view. The last section is left with con-clusions as usual.
Main Steps of the Reform
The regulatory agents have taken a very promi-nent role in structuring a phased transitionto new IR benchmaks. Indeed, in its 2014report[11] the Financial Stability Board (FSB)issued general recommendations on reformingthe major interest rate benchmarks. In that doc-ument and in the following related updates [12],the outlined main steps in the reform can besummarized as follows:
• Actions to strengthen the current IBORs
• Actions to develop the alternative risk-free benchmark rates
• Actions to ensure contractual robustness
Reforming the IBORs
In order to allow for compliance to the EUBMR, extensive reform processes have been car-ried out by the relevant authorities to the mainovernight and IBOR rates both at internationaland EEA levels.
Whilst a reform of the SONIA has provento be successful, the corresponding reform ofEONIA has been abandoned by EMMI after itsData Analysis Exercise (and the first ECB publicconsultation on developing a euro unsecuredovernight interest rate[5]) on the basis of liq-uidity, size and concentration of the market onwhich it relies.
Concerning EURIBOR and LIBOR rates in-stead, the effort of both the EMMI and the Fi-nancial Conduct Authority (FCA) of transform-ing them in transaction-based benchmarks haveproven to be unsuccessful (see [8] and [12]) be-cause the market for unsecured wholesale termlending to banks is no longer sufficiently ac-tive. The FCA has therefore decided that, aftera 2021 deadline agreed with the LIBOR panelbanks, it will no longer try to persuade or com-pel them to contributing to the benchmark de-termination. EMMI, instead, recently developeda hybrid three-level waterfall methodology forEURIBOR determination in order to underpinto the greatest extent possible its determinationby transaction data, as required by the regula-tion (see [9] and [10]). A real data testing phaseis expected to have ended in August 2018 anda second consultation paper will be probablypublished in the coming weeks. In any case, theimplementation of the new methodology will beconcluded by Q4 of 2019, in time for applicationto authorisation under the EU BMR.
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Financial Area RFRs Typology Available AdministratorUSA Secured Overnight Financing Rate (SOFR) Secured Y Fed NYUK Reformed SONIA Unsecured Y BoEEU European Short-Term Interest Rates (ESTER) Unsecured N(*) ECBJAPAN Uncollateralized Overnight Call Rate Unsecured Y BoJSWITZERLAND Swiss Average Rate Overnight (SARON) Secured Y SIX Swiss Exchange
TABLE 1: New Risk Free Rates chosen in the main financial areas. (*)Regarding the Euro Area, although Pre-ESTER is
already available with data going back to March 2017, the official publication of the ESTER will not take place before
October 2019.
Alternative IR Benchmarks: Risk Free Rates(RFRs)
The EONIA dismissal, the uncertainty over theEURIBOR compliance with the EU BMR and theFCA decision over the LIBOR supervision dis-continuation have created a significant pressureto both the financial market and the supervisoryagents, which are responsible to watch over thesystemic financial stability, to develop a newrange of interest rate benchmarks that are com-pliant with both the IOSCO Principles and theirlocal regulatory implementations (EU BMR forEurope). As requested by the IOSCO Princi-ples and under the coordination of the FSB, RiskFree Rate Working Groups (WGs) have been estab-lished around the world to select new (fallback)interest rate benchmarks: they are composed ofmarket participants and supported by supervi-sion agents as advisors.
Due to the current state of the unsecuredmoney market and for the ease of interpreta-tion, the new benchmarks have been chosen tobe as close as possible to risk-free rates. Ta-ble 1 summarises the RFRs chosen in the mainfinancial areas.
Time to Transition is Now
Given the 2021 deadline agreed by FCA withthe LIBOR panel banks, and the importance ofthe topic in terms of scope and challenges, wethink that the right time to transition is now.
One of the main recommendations of theFSB to WGs is to develop effective transitionplans and strategies in order to:
• minimize market disruptions;
• create and sustain demand and liquiditysources in hedging markets for the newRFRs.
Beyond recommendation, it is up to the in-dustry to ensure a clear and smooth transition.To this purpose a recent survey published bythe International Swaps and Derivatives Associa-tion (ISDA)[14] is interesting since it involves
150 market participants among banks and otherusers and reveals that there is a significant gapbetween the general awareness of benchmarksreform and the actual steps being taken to itsimplementation. Although more than 50% ofsurvey participants declares having initiated in-ternal discussions on the topic, just 11% hasallocated real budget and resources for the tran-sition programme.
The awareness of the implications such areform may have within the frameworks of thebanks is a crucial point in order to develop ef-fective transition projects. The magnitude of thechange is high since it involves around $ 370trillion across derivatives and other cash prod-ucts (like bonds, loans and securities) related toIBORs, and can affect different aspects of dailybusiness operations. On the other hand, timeis running out because banks have just 3 yearsto be fully compliant with the new IR bench-marks: they should start allocating budget andresources in order to handle with the transition.
In what follows we briefly discuss two mainkinds of implications related to the transition:
1. Business Implications: potential effects ofthe transition on the way in which exist-ing contracts will be handled and newcontracts will be stipulated by banks.
2. Technical Implications: potential effects ofthe transition on the technical aspects ofdaily operations, with focus on the typicalFront-to-Risk chain of a bank framework.
Business Implications
Contractual Robustness
A key role in the transition will be played by theability of WGs (administrators and market par-ticipants together) to guarantee the contractualrobustness in:
• handling the new contracts;
• handling the legacy contracts.
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Regarding the new contracts, in order to beable to use the new benchmark rates for valu-ation purposes, a liquid market on new refer-enced OIS (and relative basis swaps, for tran-sition purposes) should be first established. Inthis context the Alternative Reference Rates Com-mittee in the US (ARRC) and the Working Groupon Sterling Risk-Free Reference Rates in UK envis-aged an effective transition strategy focusing onthe new transaction in order to create liquid-ity and minimize disruptions: derivatives refer-enced to SOFR and SONIA have been alreadycleared by some CCPs, in addition the World’sBank has recently been able to issue and hedgea SOFR-referenced Floating Rate Note.
For the Euro Area instead, an official RFRshas only recently been chosen by the WG [5].Although historical data of the preliminary ver-sion of the ESTER (i.e the pre-ESTER) are avail-able since August 2016, an official version of therate will probably be published by the ECB onlystarting from October 2019. This means that theEuro Area will only have three months to createa sufficient liquidity for instruments referencingthe new RFRs to allow a transition as frictionlessas possible. This has to be compared with the3.5 years’ time that other RFRs, such as SOFRand reformed SONIA, are having to accomplishthe same goal. Uncertainty regarding the pos-sibility of creating and sustaining demand andliquidity for the new EUR RFRs will rise thecosts of the transition itself and generate issuesin the handling of new contracts.
Regarding the handling of the legacy con-tracts, the FSB Official Sector Steering Group(OSSG) is pushing market participants to in-crease contract robustness of various financialproducts against the risk that a widely-used in-terest rate benchmark could be discontinuedpermanently. In the October 2017 report[12]OSSG has recommended the following high-level principles in reviewing possible fallbackprovisions:
• to the extent possible, the contractual pro-vision should seek to avoid any disconti-nuity in valuations in the event that thefall-back is triggered, minimizing the im-pact on valuations and then avoiding anypotential disruption to financial stability;
• the contractual provisions must be robust,sensibly safeguarding against either anypotential for manipulation or potential fornoisy data or the methodological construc-tion of the spread itself to allow the fall-back to clearly deviate from what most
market participants would construe as areasonable or fundamental value for anIBOR swap;
• any method should not impede, to theextent possible, any efforts towards volun-tary transition.
In that context ISDA is taking initiatives atinternational level to implement robust contrac-tual fallbacks for derivative instruments thatwill account for permanent discontinuation ofcurrent benchmarks, together with a protocolto amend legacy contracts. The contractual fall-backs will rely on the use of the new relevantRFRs subject to term and spread adjustments.ISDA launched a market-wide consultation onthat in July, proposing four options to adjust theRFRs (moving from a term rate to an overnightrate) and three potential approaches to add aspread (in order to reflect differences in the bankcredit risk premium and other factors).
This sort of fallbacks implementation, beingdone to align with the Article 28(2) of the Bench-mark regulation[6], should however also applyfor EONIA and EURIBOR, for which a RFRs isnot currently live. Therefore, an interim 2018Benchmark Supplement is currently being pre-pared, also with the support of a three months’consultation.
ISDA efforts on developing robust contrac-tual fallbacks are absolutely comprehensible.Despite the awareness of the fact that IBORs con-tribution can be interrupted after 2021, existingdeals on IBORs still continue to be traded andnew ones will be created until 2021: without asafety net the potential sudden discontinuationof IBORs would generate disruption in marketvaluations. Moreover, effectiveness of contrac-tual fallbacks will depend also on the indus-try consensus on appropriate spread and termadjustments: consultation launched by ISDAis pushing in that direction with the purposeof reaching a firm-wide consensus on fallbackmethodologies.
Governance
Another important point banks and marketpractitioners should consider carefully is theGovernance.
The most complex part in defining a robusttransition strategy is not to find the right fall-back itself, but rather to implement a smoothtransition process able to provide clear condi-tions in order to:
• identify proper fallback rates;
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• identify the proper methodologies to befollowed to switch to fallbacks;
• identify the triggers for fallback applica-tions.
Clear and well-defined Governance pro-cesses within financial institutions will supporta smooth transition minimizing the probabilityof market disruption due to the lack of contrac-tual robustness.
We have already explained that the scopeof the transition is extremely large, due to thefact that several asset classes are now relyingon IBORs. In addition to strengthening, Gov-ernance processes should have a key role alsoin harmonizing fallback arrangements amongdifferent financial instruments. The currentframework of fallback provisions is not appro-priate to face a sudden cessation of IBORs, more-over it suffers a lack of consistency between ar-rangements for cash products and their deriva-tives hedges: a robust process of Governanceshould prevent weaknesses by implementing abetter and more consistent safety net.
FSB[12] is clearly concerned about this topicand stressed the need of sound Governance pro-cesses among market participants to preventdisruption. While ISDA is taking care of thetopic for derivatives contracts internationally,the enhancement of fallback arrangements fornon-derivative instruments is left to each mar-ket participant: the need of clear, robust andshared Governance processes is essential morethan ever.
Technical Implications
Based on the several articles published on thetopic in the last months, this transition maygenerate challenges in the valuation and riskmanagement fields including potential issuesrelated to the fact that existing transactions willbe affected. However, from these articles it isdifficult to find a clear explanation on how andwhere this transition can hit a bank within itsframework.
From a pure Risk Management perspective,the transition from IBOR-based to new referenceRFRs poses several challenges to be evaluatedcarefully by financial institutions.
Considering the traditional Front-to-Riskchain, we try to identify the most relevant impli-cations of the transition by phase:
1. Market Data and Valuation.
2. Risk Scenarios Calculation.
3. Impacts on Risk Metrics.
We will focus more on the Euro area, withsome examples on the EONIA-ESTER transition,even if most of the challenges can be consideredin common with the reforms in other financialareas.
Market Data and Valuation
In this phase there are two main implications abank should take into account:
• the dismissal of current IBOR rates contri-bution;
• the contribution of new RFRs and relatednew curves construction.
Regarding the first point, starting from 2020EONIA publication won’t be guaranteed any-more, as well as LIBORs in 2021. It implies thatdata source systems could stop maintaining thecontribution and the configuration of relatedinterest rates curves to the downstream systems.This could be a problem for legacy contracts thatexpire after 2020-2021 and won’t be convertedto the new RFRs. Banks should prepare theirIT and Risk Management infrastructures in or-der to analyse the best solution to this potentialcase, in line with Front Office desks, in orderto minimize pricing misalignment and relatedmarket disruption.
The second point is surely the most challeng-ing, since it requires the management of newmarket data and new curves construction. Themain implications here could be summarized asfollows:
1. Prepare the Risk framework to receivenew input data from Source Systems.Collect, check, maintain and storage thedata in the IT infrastructure followingthe proper Governance processes; in ouropinion this implication won’t represent areal challenge, especially for medium andbig banks, since nowadays financial in-stitutions are already prepared to receiveand manage significant amount of marketdata.
2. Construct the new interest rate curves.This is the real challenge of this transitionfor two main reasons:
• Data availability: lack of data in aproper granularity;
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• Liquidity: uncertainty about the liq-uidity of the market for the newRFRs.
Both these two elements can undermine aproper curve construction, which is the basiccondition for a proper pricing valuation.
In our opinion data availability is the mostrelevant challenge that banks have to face giventhe need to build the term structure of the newrates.
Some market participants stressed the atten-tion to another potential issue: the absence ofa well-established industry consensus may gen-erate multiple competing definitions of termrates and, as a consequence, multiple alterna-tive competing approaches for forward-lookingterm structures modelling. We think this is nota real issue at least for the following reasons:
• regulators and international supervisorsare stressing the need of a Governance fora wide-spread market consensus on thenew RFRs benchmarks construction, issu-ing principles and recommendations thatgo in that direction;
• ISDA is seeking to obtain the mostwidespread consensus among market par-ticipants as possible in order to select themost appropriate manner to add term andspread adjustments, if a term rate is to bedetermined from a reference RFRs;
• disclosed methodologies for SOFR, SO-NIA and ESTER calculations (just as ex-amples) are similar each other and basedon actual transactions data.
The recent selection by the Euro RFRs WGof the ESTER rate as a substitute for EONIA asRFRs was mainly driven by the fact that:
• it will be managed directly by ECB (ex-cluding any potential conflict of interest re-lated to private company administration),with data coming from the MMSR Reg-ulation [3] [7], the regulation concerningstatistics on the money markets;
• it captures banks overnight borrowingcosts on the basis of transactions with bothbanks and non-banks financial counterpar-ties (while EONIA currently is excludingall transactions with non-banks);
• it is computed as a volume-weighted av-erage of real transactions conducted at
arm’s length, consisting of overnight un-secured fixed rate deposits with volumesbeyond EUR 1ml (becoming de-facto morerepresentative of money market transac-tion than current EONIA).
ECB is expected to officially publish the firstfixing by October 2019. In the meantime, it hasstarted to publish a pre-ESTER for research pur-poses and, in a sample of daily observationsbetween March 2017 and May 2018, the spreadbetween pre-ESTER and EONIA proved to bequite stable around 8/9 bps. If this spread willactually remain constant, also the technical im-plications of building the new curve could beeasy to face, since it would be possible to figureout some linear relationships between the twobenchmarks.
However, many external factors could gen-erate shifts in EONIA, and consequently inthe ESTER-EONIA spread. Examples couldbe the change in ECB monetary policy (withsubsequent impact on excess liquidity) and thechange in banks credit spread levels, interre-lated if we consider Systemically Important Fi-nancial Institutions. As also reported by Gold-man Sachs in a recent research published in Au-gust 2018[13], statistical relationships betweenthese variables can be identified, but they arenot completely reliable at this stage due to thelack of a more representative data sample: thisposes a real challenge in finding a stable solu-tion for new curves construction starting fromcurrent EONIA values.
Risk Scenarios and Calculations
In addition to the challenges posed by the newcurves construction and the liquidity of the newRFRs markets, banks should consider the factthat these new benchmarks won’t have enoughhistory in the first years of the transition to buildreliable historical scenarios, with potential im-pact in terms of valuation of:
• the Risk Metrics that rely on historical sim-ulation (e.g. VaR metrics for both manage-rial and regulatory Market Risk purposes);
• the dynamics and historical modelling ofthe volatility (e.g. Swaptions pricing).
In such a case Risk Management depart-ments should minimize disruption events byfinding acceptable proxies or introducing newvaluation techniques. Most of the solution willdepend on how the risk managers will decide
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to manage new curves construction, if relyingon statistical relationships with current IBORvalues or working on completely new data (seethe EONIA-ESTER spread example discussedin the previous paragraph).
It is crucial also in this case to find out so-lutions that are commonly spread and sharedamong market participants in the financial in-dustry.
Another challenge could be faced during thetransition period when the IBORs will be nei-ther dead nor alive. Banks will be probablyforced to model and maintain three kinds ofcurves in their risk management systems:
1. the current IBOR-based ones,
2. the current OIS-based ones,
3. the new RFRs ones,
and the respective basis between each pair.This could be an issue indeed, especially
when financial institutions have to performdaily calculations for risk management pur-poses and there will be both IBOR and RFRs-linked products in the books to be re-valuated.
It will surely be the case in the euro areawhere at the moment the transition will seeEONIA replaced by ESTER by 2020 and the re-formed EURIBOR kept alive. In our opinion thissituation can get worse in case of illiquidity inthe new RFRs: it can generate a basis betweenthe actual bank funding rate and the theoreticalfunding rate given by the new benchmark. Alsothis potential funding basis should be takeninto account by the Risk management of thebank during daily calculations.
Impacts on Risk Metrics
The transition will obviously generate an impacton the currently calculated risk metrics:
• for Trading Book products both VaR andSensitivities (like DV01 and Vega Risk)will be affected by market risk perspec-tive, and for Risk Managers it will be fun-damental to understand the materiality ofthese impacts in the control of manage-rial limits to daily trading activities. AlsoCCR and CVA risks could be affected, di-rectly inheriting the impacts from basepricing valuations;
• for Banking Book the transition will af-fect a huge amount of cash products like
Bonds, Loans and other securitization in-struments; impacts must be evaluatedcarefully in terms of both liquidity andinterest rate risks.
It will be crucial for banks to understandthe overall impact of this transition on theirbooks in terms of RWAs and current regula-tory capital charges. For example the lack ofhistorical data on the new rates may have animpact in the light of new market risk regula-tion for trading book (FRTB), where a crucialpoint for metrics calculation is the distinctionbetween “modellable” and “non-modellable” riskfactors. For cases like ESTER-EONIA, banks inthe euro zone can start performing some impacttests by assuming a relationship between thecurrent and the new benchmark on the basisof the quantitative data provided by the ECB.Due to the concerns we have highlighted inthe previous paragraph, impact tests should bebased on some methodological and technicalassumptions, but it is fundamental for banks tostart working on it before EONIA contributionscease in order to prevent potential non-desirableimpacts on risk metrics. Indeed, banks could ac-tivate working groups and discussions directlywith ECB and national regulators in order to setup first impact tests (with related assumptions)and then understand how this transition canaffect current risk capital charges.
Another important point to take into accountis the basis risk deriving by this transition. Itcan arise at two different levels:
1. The adoption of new RFRs occurs signifi-cantly more quickly for derivative instru-ments than cash instruments, generatinga situation in which different asset classesare exposed to different rates and a basisrisk needs to be considered in hedgingstrategies.
2. The fact that different RFRs can beadopted by different currency areas at dif-ferent points in time can generate cross-currency basis risks for global players;also in this case, a robust Governance pro-cess agreed worldwide could really sim-plify the management of this basis risk byarranging the different transition strate-gies in a shared timeline.
Conclusions
The termination of IBORs contribution in thefinancial market is no more a remote possibil-
Issue n. 14 / 201815
New Market Standards
ity but it is becoming a real scenario. That iswhy we think time to transition for banks isnow: beyond the awareness of the importanceof such a reform, banks should start now allocat-ing budget and resources to implement robusttransition strategies within their frameworks.
At general business level, a lack of contrac-tual fallback robustness in the transition cangenerate widespread market disruption, that issomething strongly non-desirable. A worldwidecoordinated action of Governance (like the oneISDA is doing for derivative contracts) is reallybeneficial in order to set up a better safety netand guarantee a smooth transition.
Focusing more on technical details withinthe Risk Management fields, the transition to
new RFRs implies the need for the banks to up-date their frameworks in order to collect newdata properly and manage the multi-curve mod-elling. Also in this case a coordinated actionamong all market participants can be really use-ful in identifying the best methodologies andtechniques to minimize impacts on risk metriccalculations and capital charges.
Finally, in addition to the implications wehave tried to outline in the possible clearestway, we suggest banks to take this transition asan opportunity to optimize their current riskframework processes in order to reduce com-plexity and increase efficiency.
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References
[1] Board of the InternationalOrganization of SecuritiesCommissions. Principles forFinancial Benchmarks. July 2013.Available online at:https://goo.gl/Fi2qqp.
[2] European Central Bank. PrivateSector Working Group on EuroRisk-Free-Rates Recommends ESTERas Euro Risk-Free Rate. September2018. Available online at:https://goo.gl/nzz3Tz.
[3] European Central Bank. ESTERMethodology and Policy. 2018.Available online at:https://goo.gl/n6QsQq.
[4] European Central Bank. SecondPublic Consultation on thePublication by the ECB of anUnsecured Overnight Rate. March2018. Available online at:https://goo.gl/WAiBZ1.
[5] European Central Bank. FirstPublic Consultation on thePublication by the ECB of anUnsecured Overnight Rate.November 2017. Available onlineat: https://goo.gl/WjmyH4.
[6] European Parliament and TheCouncil of European Union.Regulation (EU) 2016/1011. June2016. Available online at:https://goo.gl/q6XsQK.
[7] European Parliament and TheCouncil of European Union.
Regulation (EU) 2014/1333.November 2014. Available onlineat: https://goo.gl/Jr1jXs.
[8] European Money MarketsInstitute. Pre-Live VerificationProgram - Outcome and WayForward. May 2017. Availableonline at: https://goo.gl/9jVkCm.
[9] European Money MarketsInstitute. Consultation Paper on aHybrid Methodology for Euribor.March 2018. Available online at:https://goo.gl/LMLrmF.
[10] European Money MarketsInstitute. Consultation Paper on aHybrid Methodology for Euribor -Summary of Stakeholder Feedback.June 2018. Available online at:https://goo.gl/K4JSsY.
[11] Financial Stability Board.Reforming Major Interest RateBenchmarks. July 2014. Availableonline at: https://goo.gl/VortJB.
[12] Financial Stability Board.Reforming Major Interest RateBenchmarks - Progress Report onImplementation of July 2014 FSBRecommendations. October 2017.Available online at:https://goo.gl/GZ7STx.
[13] Goldman Sachs. European Views:Explaining the Euro Short-Term Rate(ESTER) spread to EONIA.Economic Research. August 2018.
[14] International Swaps andDerivatives Association. ISDAQuarterly. Vol. 4, Issue n. 2, August2018.
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New MarketStandards
An overview of BREXIT effects on the BankingSystem
Argo Magazine
About the Authors
Elia Stucchi:Business Analyst.As Business Analyst, he currently workswithin Iason team to support a bigpan-European Bank. In particular, he followsthe definition of satellite models, thedevelopment of scenario analysis andmanagement of Regulator requiredmethodology. Furthermore, he works onproject concerning the Market andCounterparty Credit Risk.
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New Market Standards
An overview of BREXIT effectson the Banking System
aaaa
Elia Stucchi
T he decision by Great Britain to leave Europe is certainly an extraordinary event. Following what hasbeen proposed by some Regulatory Opinions and some already developed works, this article presentsa brief overview of the systemic effects for the Banks active in the Community market and in the UK.
The effects of the so-called BREXIT can be observed in all the operating levels of the Banks and will determinethe need, by the Institutes, to develop a series of procedures to mitigate the risks inherent in this event.2
The banking system, after the economicand financial crises, is under stress fora further important reason: BREXIT.
British citizens, during the referendum heldon 23 June 2016, expressed their willingnessto leave the European Union; this decisionhas had, and in large part will have, political,economic and social effects. One of the mainsectors affected by the exit of UK is the bankingworld, an important segment for the Britisheconomy and more generally for the world one.As reported in documents published by theEuropean Banking Authority "EBA" [1] [2] andby the European Central Bank “ECB”[5] , it isclear that BREXIT will have important effectson the daily banking activity of the Institutes. Ifas assumed by the Authority a so-called "HardBrexit" occurs, i.e. an exit without agreementsbetween the parties, the induced risks will re-quire changes and internal control structures(no “empty shells”) advanced and able to mini-mize risks and negative effects on the bankingsystem, and therefore on the economic andindustrial one. The objective of this brief paperis to propose an overview of the effects thatBREXIT, whether with or without agreements,will have on banking activities, on their balancesheets and therefore on the possible effects thatconsumers will be able to directly observe.
Who? Actors Involved
To the effects of BREXIT, it is necessary to ob-serve which actors will be more affected becauseof their presence on the European market. TheFigure 1 shows how different subjects, strictlyinterconnected and integrated, operate withinthe European Union and the United Kingdom.
Due to the British exit from the EU, this inter-connection will be severely tested and a series ofagreements will be needed in order to define anew operational framework. These agreementswill be important for the continuation of the re-lationship between Counterparts and necessaryfor economic growth and stability. The financialinstitutions that will be impacted by BREXITcan be divided into three distinct categories:
1. European banks and their respective sub-sidiaries in the UK;
2. UK based banks and their respective sub-sidiaries in the EU;
3. Non-EU banks and their respective sub-sidiaries in the EU and UK markets.
2The following article includes ideas and opinions that cannot be proved by any real data or fact-checking yet, since basedon hypothesis and discussions currently ongoing in the financial industry. The main purpose of this article is to focus onpotential outcomes of Brexit on the banks’ activities but is not aimed at evaluating or criticizing in any way the politicaldecisions in relation to those event.
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FIGURE 1: Actors Involved
In the absence of agreements among Coun-terparts, Governments and Regulators the cur-rent relationships will possibly deteriorate withsevere consequences. The European Regulatorshave already pointed out that opinion warningall the involved Subjects.
From the EBA guidelines of June 2018:
"The EBA is issuing this opinion in response tothis unprecedented situation, considering the poten-tial for disruption to financial institutions and theircustomers if the financial institutions are not ade-quately prepared poses serious risks to the objectivesgiven to the EBA”
It is important to underline two words thatremark the importance of this paper: unprece-dented and potentially disruptive. Then, accord-ing to those statements, all of the previouslydefined actors will be potentially affected bythis event. The EBA, through its guidelines,highlights how institutions must be well pre-pared and need different guidelines to mitigatethe risks.
The EBA opinions have two fundamentalobjectives:
1. To prepare all the EU27 and UK financialinstitutions for BREXIT (with or withoutagreement) and then to equip them withguidelines to structure all the instrumentsaimed at mitigating risks and negative ef-fects; they will strongly influence not only
the activity of financial institutions butalso that of Corporations, Governmentsand Consumers;
2. To protect bank customers exposed to thisparticular financial event. Customers willsuffer the effects of an extraordinary eventthat could change the actual (and rela-tively well known) situation. Banks couldimplement robust and sound decisions toinfluence directly Customers views andactivities.
Regarding the first purpose, banks will haveto carry out a series of assessments and activ-ities as a result of the possible increase in riskon the financial and economic markets. First ofall it is important to have full knowledge of thecontracts in place for the whole of the Group’ssubsidiaries and with external parties, or thosewithin the EU and the UK market. All existingcontracts (mortgages, credit cards, investments,etc.) must be protected and continuity in theactivity must be facilitated, in the path knewas"business-as-usual". The general assessmentmust also concern solvency and liquidity as-pects of the Institutes’ positions, inter-grouprelations, market position and business model.Moreover, in order to respond to the riskinesssituation it will be necessary to check the Cap-ital level and requirements held by the Bank.Ensuring full coverage of the risks subscribed bythe Banks, increasing (for example) the levels ofcapital to guarantee particular instruments thatare supposed to be effectively stressed (see thefollowing part concerning the role of the clear-
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New Market Standards
ing houses and derivative products). Two otherimportant aspects highlighted by the EBA are:the governance structure and the funding capac-
ity. Banks must have a structured organizationand control activities can not be outsourcedcreating, by quoting the note, subjects similarto "empty shells". This organizational structurewill be able to analyze all the effects on theInstitute’s booking model. The Bank must alsobe able to maintain the ability to find resourcesand funds even in the event of a BREXIT with-out agreement between the parties, evaluatingits rolling activities, other possible sources offinancing and any effects on its business activity.
The second objective of the guidelines re-gards the protection of consumers, shareholdersin financial institutions. All the informationconcerning the effects of Brexit on consumersinterests and their activities must be providedto them. In addition, banks must clearly in-dicate which strategies and behaviors will beimplemented to minimize impacts; moreoverthe EBA emphasizes the importance of clarify-ing, analyzing and explaining all the possiblecontractual changes that would affect the con-sumers, so as to make them participate in thegeneral situation.
What? The BREXIT Effects
It is clear that there could be different effectsthe Bank may be prepared to face. We try to un-derline the most important by different blocks,in order to well illustrate the possible conse-quences on the various operational aspects:
• Credit Area: the impact will concern theriskiness of the credit portfolio and in gen-eral the credit process of the Institutes;
• Internal Model;
• Capital Markets: impacts on trading activ-ity and hedging transactions may occur;
• Funding Cost: effects on funding activitiesof the Banks and related costs;
• IT infrastructures and governance.
The consequences might be greater for thoseSubjects and Counterparts that operate in coun-tries more exposed to British economy; more-over the effects related to the portfolio exposureof the Banks would depend on country’s con-centration and diversification. As reported in
different studies, among which it is possibleto cite the work of Luigi Federico Signorini forBank of Italy[3] , there will be different impactfor European and World Countries after BREXIT.In addition, Standard & Poors has defined theBrexit Sensitivity Index (BSI)[4] : an indicatorthat clearly provides which countries are mostsensitive to a British exit from the Union. Thisindicator uses information regarding, for exam-ple, the import/export and investments levelof the various countries within the UK, migra-tion information and financial shared interests; it can be a good proxy-indicator of generalsynthesis and can be a point of reference forthe different subjects into the market. From theS&Ps analysis, the countries most affected fromBritish leave will be those who closest from ageographical point of view and those histori-cally connected to the British economy; so itis easy to cite as example like Ireland, Malta,Cyprus and the countries of Northern Europe.
Effects on Credit Risk Area
Following the previously depicted point, the oc-currence of the BREXIT may have an importantimpact on the credit area of the Institutions,thus impacting directly on the indications in thefinancial statements, on the current activity andtherefore on the implemented business model.It is clear that the economic and financial effectscaused by the exit from the Union will be veryimportant for the credit portfolio held by banks.In particular if the exit occurred without anagreement between the parties, there could bea downgrade of the subjects operating in thesemarkets more exposed to the British economyand those operating in the UK; the downgradewill occur following the general increase incredit risk due to more difficult economic condi-tions in which some parties will find themselvesmore easy not to fulfill their obligations towardsthe Institutes. This phenomenon will have twoimportant impacts: the loan portfolio credit
quality and the provisioning activities imple-mented by the Bank. Within this riskier environ-ment, any downgrade of some Counterpartiesmight corresponds to a greater Probability ofDefault associated with them. This will sup-posedly lead to a less stable and riskier CreditPortfolio (with a deep focus on those subjectswho have ties and dependence on the Britisheconomic market). A deterioration in creditquality will clearly influence the definition ofassets in accordance with IFRS9, according to
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which the portfolio is divided into "Held tocollect" and "Held to collect and sale" assets; asdepicted from the directives and from the regu-lation, in order to correctly evaluate the qualityof a specific loans, it is necessary to incorporateinto the calculation the future loss evaluated forthe loans (overcome the past idea of “incurredloss”). So an increase in the overall riskiness,for example shown by a worsening in creditindicators associated to some Counterparts, willdetermine a variation within the staging of thecredit activities and therefore in the subsequentprovisioning activity that the bank will have toimplement. The Capital requirements necessaryfor adequate credit risk coverage, have beenmodified and more own funds will be neededwith an immediate effect on the activity of theInstitute. In the matter of loans, by debtorsoperating with the UK market, it will be moredifficult to repay them and therefore the bankswill be considered unable to meet the obliga-tions undersigned by the Subjects. Besides thebanks should be able to implement not onlythe aforementioned provisioning operations butalso different business and commercial policiesdue to the changes into credit Portfolio; theyshould facilitate loans diversification and thusminimizing the associated concentration riskslinked to the overall exposures.
Effects on Internal Models
The topic related to the analysis of the Creditand the riskiness ensured to it, introduces avery important theme: the one related to theuse of Internal Models. All of the institutionsinvolved will need to have specific approvalsfor the use of internal models for the evaluationof the different processes. In fact, there may bedifferences between UK-based and Europeanassessments; from this point of view, collabora-tion between the UK and EU27 is necessary inorder to share all the information and processesnecessary to maintain consistency in the evalua-tions carried out by the internal models.
Effects on Funding & Liquidity
Another aspect closely linked to Brexit con-cerns Capital and Liquidity requirements andthe internal control implemented by bankinginstitutions. It is clear that in the absence ofagreements between the parties there will beprobably financial tensions on the markets that
will directly influence the operations of thebanks. An important aspect is strictly con-nected to the interbank market; it is not sodifficult to think that an increase in economictensions and general risk can have a strongimpact on the rates with which banks lendmoney to the market. As happened in 2011,it is possible to have situations of difficulty inobtaining the liquidity necessary to support thedaily banking activities; the Central Banks canthen carry out policies aimed to maintainingliquidity within the system and improving thefinancing conditions of the Subjects. With this inmind, the so-called Contingency Funding Plansare inserted, aimed at mitigating the liquidityrisk associated with any stressful situations,such as BREXIT. Banks, especially those operat-ing in the British market, will have a series ofbuffers to deal with high stresses at least in theshort term; then having a strong "Liquidity RiskManagement" structure is also very importantand must be more structured and integratedover the Group’s branches . Banks may face astress regarding the levels of capital held; thefinancial tensions and the greater riskiness ofthe system can lead to demand greater levelsof capital held. In fact it will be presumablymore onerous, to hedge the transactions onfinancial markets and to finance subjects operat-ing in markets whose the intrinsic risk is greater.
Effects on Capital Markets
The effects of BREXIT can also be observedinto the Financial Activities of the Banks. Oneaspect that needs to be analyzed, as highlightedalso by the ECB[5] , is connected to the BookingModel of the Institutes; that regards the correctinternal control of associated risks of the activi-ties of the Institutes and shared by all the GroupBranches. Indeed all the Subjects involved inback-to-back operations must have a structurecapable of correctly considering all the imple-mented activities: differentiating between theso-called onshore and remote banking operations.The onshore concern all those EU activities andproducts exchanged between EU customers;while the latter concern operations with thirdcountries. This correct assessment of the ac-tivities affects the risk profiling and adequatehedging procedures, necessary for compliancewith the European Directives. A further aspectto analyze is related to the derivatives marketand the role played by the Clearing Houses inthe market stability. As proposed into a Paper
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New Market Standards
made from the International Swaps and Deriva-tives Association “ISDA”[6] , with BREXIT theremay be problems that have not been observeduntil now due to the fact that actually Banksare using Clearing House operating in UK fornumerous (almost all) operations on derivativeproducts (IRS, CDS, Swap etc). The key pointsare basically two: legal framework and oper-ative aspects. It will be important to analyzethe agreements that will regulate the existingand future contractual obligations; it is difficultto imagine that the contracts with an extra-EUcounterpart will be declare not compliant butit will be necessary to know in depth the newregulatory framework. Moreover it will be nec-essary for the Banks to decide whether to keepin the UK as a clearing house or to move theiractivities on the derivative markets with otherplayers. This choice will depend on variousfactors related to possible EU-UK agreementsand the analysis of costs and benefits profileof this operation. There may be competitionphenomena between the Clearing House ofEuropean countries and non-EU subjects, eachof which will try to get the largest number ofcustomers who will decide to move operationsfrom London. The actual central role of LCH(based in London) could be undermined bydifferent players from different countries likeU.S, France and Germany; examples could bethat Banks will move their operation to EurexExchange, a clearing house located in Frankfurtor to CME that operates from the United States.
Furthermore, one important aspect concernsthe FX market. There may be a strong pounddevaluation and this would lead to differenteffects on the financial statements of banks andtheir operations. First of all, this devaluationwill lead to a revaluation of assets denominatedin pounds with clear effects on the balancesheet, and there will also be important effectson the operations of the client companies ofbanking institutions. Infact, depending on thebusiness and the import/export levels, therewill be immediate and clear effects following apossible devaluation. The exporting companiesto the English market will be strongly affectedby the loss of English purchasing power. Onthe other hand, the companies importing fromthe British market will be able to benefit froma more favorable exchange rate (all this whilekeeping clear the fact that there will no longerbe a single market, free and accessible as beforethe English choice).
Banks and all branches, will have to closelyanalyze the portfolio held and observe whichcompanies will be most affected by this choiceof monetary policy; therefore trying to min-imize the portfolio impact and consequentlyany negative effects on the business. This willhave effects on equity investments on particularsecurities affected by BREXIT which will haveto be controlled through a careful asset alloca-tion. A further aspect linked to the financialframework is related to all those companies,operating in the UK, that today benefit frompossible European Community Funding; thosefunds, in the absence of bilateral agreements,won’t be secure and companies could face inwith a decrease (or an annulment) of these.Thus creating important effects on financingpolicies and planned investments. Banks willtherefore have to carry out an increasingly deepand continuous view on portfolio investmentsand Counterparties structure.
Another important aspect will concern, fol-lowing the definition proposed by the Regulator,to avoid "Empty Shells" phenomena; strictlyrelated to the correct evaluation of back-to-backoperations as previously depicted. That is asituation in which some branches of a bankinggroup do not have an effective operational struc-ture in order to work with the Bank. As pro-posed from the Regulator, all the structures ofInternal Governance and Management must becarefully developed for each branch. Branch’sstructure will be developed and able to analyzeand control risks, allowing a capillary controlof all the Group’s activities. Moreover the Reg-ulator outlines the impossibility of outsourcingall the management activities of the Banks; theInstitutes must have an important managementbody capable of correctly managing all theGroup’s problems, in particular with a focuson managing the banking activities associatedrisks. This internal control must allow all theunits of the Group to be able to overcome anystress and crisis events in compliance with allthe regulations currently in force. The develop-ment of control and governance systems mustbe accompanied by an increasingly integratedand developed Management Information System;the internal structures must define a set of re-ports and in-depth documents that will allow todefine and clarify all the activities implementedby the Group, such as the control and manage-ment of Risks faced by the Bank, the operating
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strategies and the hedging activities.
Effects on Governance & IT Structure
Related to the governance structure is the fol-lowing topic, faced by the Regulator. As pro-posed in a paper called SNRA[7] ("Suprana-tional Risk Assessment") it has highlighted therisk of money laundering and financing to terroristorganizations. In the event that some Banks de-cide to move from the UK to a State belongingto the Union, they will have to comply withEU Directive 2015/849 (so called "IV Directive")which provides for a careful control on bankingactivities in order to avoid the aforementionedphenomena and to limit the risk associated withthem. Another issue is related to the storage ofData and the IT-infrastructure of the Banks; incase that the Institutes transfer some activities,the proprietary databases must be protected,avoiding loss of data and information that coulddamage the operational activity and the cus-tomers. The banks must therefore have veryadvanced data management infrastructures in-tegrated into all the branches of the group. Dueto BREXIT event, it is easy to understand howBanks, and Industries in general, could possiblydecide to move their UK branches into Union’scountries; this in order to overcome difficul-ties bringing to the separation from the single
market of the recent years. This will affect inparticular UK market and those banks who areUK based or who have different branches inGreat Britain.
Conclusions
This brief analysis has underlined how the de-cision to leave the European Union by the UKcould bring systemic effects on the banking sys-tem. The effects will affect the various areas ofcompetence of the Banks and will oblige them tomake operational and business model changes;certainly the agreements that will be carried outat the political level will be important and willnot only concern purely economic and financialaspects. The controls implemented will there-fore be quantitative and qualitative and mustcover all the business units of the Group andthe Branches thereof. It will also be extremelyimportant to define a framework of clear andshared rules between all the involved Actors; inorder to minimize the negative effects of thisunprecedented and potentially disruptive choice,keeping the overall operations unchanged andguaranteeing the interests of all of the Banksstakeholders.
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New Market Standards
References
[1] European Banking AutorithyOpinion of the European BankingAuthority on issues related to thedeparture of the United Kingdom fromthe European Union. EBA. October2017.
[2] European Banking AutorithyOpinion of the European BankingAuthority on issues related to thedeparture of the United Kingdom fromthe European Union. EBA. June2018.
[3] Signorini, L. F. Brexit: the possibleeconomic and financial effects. Bankof Italy. 2017.
[4] S&P Global Ratings Who has themost to lose from Brexit? Introducingthe Brexit Sensitivity Index. S&PGlobal Ratings. June 2016.
[5] European Central BankSupervisory expectations on bookingmodels. ECB. August 2018.
[6] International Swap andDerivatives AssociationContractual Continuity in OTCDerivatives. Challenges with Trasfers.ISDA. July 2018.
[7] European Commission Reportfrom the Commission to the EuropeanParliament and The Council. EC. July2017.
[8] European Securities and MarketAuthority General principles tosupport supervisory convergence inthe context of the United Kingdomwithdrawing from the EuropeanUnion. ESMA. May 2017.
[9] Deutsche Bank Research BrexitImpact on investment banking inEurope. Deutsche Bank Research.July 2018.
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BankingBook
Analysis of the New Standards to Measure andManage the Interest Rate Risk of theBanking Book Issued By BIS Committee
Banking Book
About the Authors
Antonio Castagna:Managing Partner and CEO at Iason ConsultingltdAntonio Castagna is currently partner andco-founder of the consulting company Iasonltd. He previously was in Banca IMI, Milan,from the 1999 to 2006: there, he first workedas a market maker of cap/floor’s andswaptions; then he set up the FX optionsdesk and ran the book of plain vanilla andexotic options on the major currencies, beingalso responsible for the entire FX volatilitytrading. He started his carrier in theinvestment banking in the 1997 in IMI Bank,in Luxemborug, as a financial analyst in theRisk Control Department. He graduated inFinance at LUISS University in Rome in 1995,with a thesis on American options and thenumerical procedures for their valuation. Hewrote papers on different topics, includingcredit risk, derivative pricing, collateralmanagement, managing of exotic optionsrisks and volatility smiles. He is also authorof the books “FX options and smile risk” and“Measuring and Managing Liquidity Risk”,both published by Wiley.
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Analysis of the New Standardsto Measure and Manage the
Interest Rate Risk of theBanking Book Issued By BIS
Committeeaaaa
Antonio Castagna
T his paper presents an analysis of the new standards issued in April 2016 by the Basel Committee, onthe measurement and the management of the IRRBB. We will investigate how the new rules will affectthe processes currently run by banks and if they are consistent with sound financial principles.
In 2004 the Interest Rate Risk of the BankingBook (IRRBB) came for the first time un-der the scrutiny of Basel Committee, which
issued the guidance document [1]. In this docu-ment, the IRRBB is defined as part of the Baselcapital framework’s Pillar 2 (Supervisory Re-view Process) and its identification, measure-ment, monitoring control by banks, as well asits supervision, should adhere to the Principlestherein set out.
An update of the (very high level) Principlescontained in the document [1] was felt neces-sary by banks and by the Supervisors, so in the2015 the Basel Committee submitted the consul-tative document [2], where two options for theregulatory treatments of IRRBB were presented:a standardised Pillar 1 (Minimum Capital Re-quirements) approach and an enhanced Pillar 2approach. The banking industry expressed, inthe feedback to the consultation, strong concernabout the the feasibility of a Pillar 1 approachto IRRBB, based on a standardised measure ofIRRBB designed to be enough accurate and risk-sensitive to set regulatory capital requirements.The Committee took into account the feedbackand decided that, given the the variegated na-ture of the IRRBB, a Pillar 2 approach would bemore appropriate.
The final document issued by Basel Commit-
tee [3] updates the guidelines of the 2005, alongthe following points: i) more specific principlesand rules are provided for shocks and stressscenarios, behavioural assumptions and the in-ternal validation process; ii) disclosure require-ments aim at a greater consistency and compa-rability of the metrics related to the IRRBB; iii)more detailed factors Supervisors should con-sider when assessing the banks’ level and man-agement of the IRRBB; iv) introduction of theconcept of “outlier bank”, identified by meansof materiality tests applied by Supervisors.
The banks are expected to implement thestandards by 2018.
Definition of the Interest RateRisk of the Banking Book
The Basel Committee document [3] sets theperimeter of IRRBB risk, confining it to thebank’s banking book positions that are affectedby the movements in interest rates. We surelyinclude in these positions all the contracts in theBank’s assets or liabilities yielding an interestrate, fixed or indexed to some market parameter,(e.g.: floating rate bonds or mortgages, but alsostructured notes), with a contractual provisionon the reimbursement of the notional capital
Issue n. 14 / 201829
Banking Book
(possibly at a discount, if it is indexed to somemarket variable and the capital is not protected).
A short definition for interest-rate sensitiveassets is provided by the document: they are all“assets which are not deducted from CommonEquity Tier 1 (CET1) capital and which exclude(i) fixed assets such as real estate or intangibleassets as well as (ii) equity exposures in thebanking book.” (see [3], pag. 15, footnote 11).On the liability side, some banks include alsothe equity in the interest-rate sensitive instru-ments, even if this is not a commonly acceptedpractice.
The interest rates’ movements cause twotypes of effects that can both entail a threaton the Bank’s current and/or future capital:
• the movements change the present valueof a Bank’s assets, liabilities and off-balance sheet items, and ultimately its eco-nomic value (EV);
• they can also change the interest rate-sensitive income and expenses, and hencethe Bank’s current and future net interestincome (NII).
The Basel document [3] identifies three typeof risk related to the IRRBB, deemed relevantfor the new proposed standards:
• The gap risk: it is produced by the differ-ent timing of the fixing of the new interestrates (i.e.: the repricing) of the instrumentsin the banking book. A mismatch (or gap)between assets and liabilities repricing cancause changes in the EV and in the NII,depending on the distribution of the re-fixing or the maturity of the instruments,and on the type of movements of the termstructure of interest rates. The main typesof movements of the interest rate curvecan be limited to three: i) parallel shift, ii)steepening/flattening, iii) change in thecurvature.
• The basis risk: it is caused by the impacton assets and liabilities that are matchedas far as the repricing is concerned, butwhose (floating) interest rates are linkedto different interest rate indices. For ex-ample a bond on the liability side and amortgage on the asset side have both thesame schedule for the repricing dates, butthe former is linked to the 3M Eonia rate,whereas the latter is linked to the 3M Eu-ribor rate.
• The option risk: it refers typically to op-tion derivative positions, but it can ex-tended also to bank’s assets, liabilitiesand/or off-balance sheet items whose em-bedded optional features can modify thelevel and timing of the related cash flows.For this reason, the option risk is furtherdisentangled into an automatic option risk,when linked to financial parameters, andbehavioural option risk, when it is producedby the behaviour of the counterparty (e.g.:depositors have the optionality to with-draw money from their sight deposit ac-counts as they like).
It is likely worthwhile to note that the Baseldocument [3] also mention a fourth type of risk,or the Credit Spread Risk in the Banking Book(CSRBB). As it is easy to guess, this risk refers,in the document’s words, to “any kind of as-set/liability spread risk of credit-risky instru-ments that is not explained by IRRBB and bythe expected credit/jump to default risk”.
If it is quite clear the type of risk it refers to,it is much more difficult to sketch a frameworkto manage and measure the CSRBB, because theBasel Committee seems to forget about it after itis introduced in the very first pages of the docu-ment. It is true it is mentioned another coupleof times, but in any case without specific prin-ciples, indications or simple suggestions aboutthe methodology the Bank should design andimplement. Some hints can be found in the An-nex 1 of the document [3], but in our opinionthey produce more confusion than clarification.
The Annex 1 of the document [3] has a para-graph devoted to the decomposition of the inter-est rate earned on an asset, or paid on a liability,by the bank. The identified components are:
1. The risk-free rate: representing the theoret-ical rate of interest an investor requiresfrom a risk-free investment for a givenmaturity.
2. A market duration spread: a premium, orspread over the risk-free rate, to remuner-ate the duration risk.
3. A market liquidity spread: a premium forthe market appetite for investments ona given duration or a given issuer, de-termined by the presence of sellers andbuyers eager to trade. 4. A general mar-ket credit spread: a premium required bya given credit quality, identified by therating of the issuers (e.g.: the additionalpremium requited for AA-rated issuers).
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4. An idiosyncratic credit spread: the pre-mium required by investors for the spe-cific credit risk associated with the specificissuer/borrower, also reflecting the assess-ment of risks related to the economic sec-tor and/or geographical/currency loca-tion of the borrower, and to the featuresof the issued instrument (e.g.: a bond or aderivative contract).
Although all these components are theoret-ically correct, it is also quite evident that theclassification is rather academic and withoutgreat practical use. For example, the risk-freerate and the duration premium cannot be dis-entangled in any meaningful way, and in theend when risk-free interest rate term structuresare extracted from market prices, they embedboth components and the risk sensitivity shouldbe measured with respect to their aggregatedchanges, which are the only observable in themarket.
Additionally, the distinction between gen-eral market and idiosyncratic credit spread isalso rather far-fetched, even if it is possible todesign a framework within which the Bank sep-arately calculates the sensitivity with respectto the general level and idiosyncratic levels ofcredit risk.
The Basel document also suggests that theaforementioned rate components apply acrossall types of exposures, but in practice theycan be more easily disentangled in instrumentstraded in the market, such as bonds, than inpure loans. For these instruments not traded inthe market, the document identifies two compo-nents that it deems more appropriate:
1. The funding rate, which is the sum of thereference rate plus the funding spread: it rep-resents the weighted average of the fund-ing rates of all the sources of the Bank tofund the loan, according to the internalfund transfer pricing methodology. Thereference rate could be a market indexsuch as the Libor or the Euribor rate thatmay include also a liquidity and generalmarket credit spread. These two compo-nents can be different for each index rate(e.g.: 3M Euribor and 6M Euribor) andalso volatile. As such they generate a socalled basis risk.
2. The credit spread: the add-on for the creditrisk related to the Bank’s counterparty,and the remuneration for other costs paidby the Bank.
The Basel document [3] acknowledges thatthe decomposition is difficult or even impossi-ble, so some of the components can be aggre-gated for interest rate risk management pur-poses. Unfortunately the suggested aggregationis in our opinion not sound for a correct mea-suring of the risks related to interest rates’ andother factors’ movements. In more detail, theBasel document proposes to consider changesto the risk-free rate, market duration spread, ref-erence rate and funding spread all relevant forthe definition of IRRBB; changes to the marketliquidity spreads and market credit spreads arerelevant to definition of CSRBB.
From the indications above, it is not clearwhether the Bank should calculate the impacton the metrics used to measure the IRRBBjointly for all components or separately. Be-sides, while it is very reasonable consideringthe risk-free rate and market duration spreadas a single factor (as we have discussed before),it is misleading including the funding marginwithin the calculation, since this quantity can-not be directly and effectively managed andhedged in reality. Actually, there is no marketinstrument that can offset the movements of thefunding spread (the Bank cannot trade a CDSon itself), and only the effect due to the qualityof the assets can be exploited for an indirectmanagement of this type of risk. We wouldrather suggest to include the monitoring of thefunding spread in the CSRBB.
We would also stress the fact that the ref-erence rate and the market rate should be de-fined in a consistent fashion. For example, if theBank decides that the risk-free market rates arerepresented by the OIS swap rates (e.g.: Eoniaswap rates for the Euro), also the reference ratesshould be considered the same market tradedrates. If the funding spread is expressed as anadd-on over another index, say the 3M Euribor,the Bank should either recalculate the fundingspread with respect to the Eonia rates, or alter-natively consider the spread between the 3MEuribor and the 3M Eonia as another risk factor(basis risk), separately measured and added tothe funding spread. The basis risk can be partof the CSRBB framework.
Finally, from the indications related to theCSRBB, it seems that the idiosyncratic creditspread is not included in the measurement ofrisks. This choice is not understandable, sincechanges in this component can have materialimpact on the expected cash-flows and theirpresent value, as we will see below. This is the
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first clue that leads us to think that the Baseldocument [3] does not consider the expectedimpact on the cash-flows produced by the de-fault probabilities, and their effects on the creditspreads. In our opinion, also the idiosyncraticcredit spread should be relevant for CSRBB pur-poses, because the total credit spread (i.e.: thesum of the general market and idiosyncraticcredit spreads) is the risk factor that shouldmonitored and whose effects measured.
We offer a different classification of the com-ponents of the interest rate paid on liabilities,or received on assets by the bank: based on thisclassification, we will identify the risk factorsincluded in the IRRBB and those included inthe CSRBB.3
Let us start with the interest rate i⇤ earnedon asset an asset with notional amount A: whenthe asset is bought from a client (debtor) of thebank or in the market, if it is a traded security,the pricing (or, equivalently said, the setting ofthe fair rate), based on the conditions occurringat the inception of the contract or the purchaseof the security, should include the followingcomponents:
i⇤A = rL|{z}ir
+ sL|{z}fu
+LBC|{z}cl
+ sA1 A1| {z }cs
+ FO + LO| {z }op
+
+ (p + #r f )E| {z }
cc(1)
where s is the average funding spread paid onall liabilities with notional amount equal to L,p = (e � r) the risk premium over the risk-freerate demanded by the equity holders for the eco-nomic capital E “absorbed” by the investmentin A, which is used for the fraction # to fundthe purchase (together with external fundingsources) and kept for the remaining 1 � # in arisk-free investment (the shareholder require areturn e on the equity). The components are:
• ir: the risk-free rate, entering in the thetotal funding cost to pay on liabilities;
• fu: the funding costs due to the spreadspaid over the risk-free rate on liabilities;
• cl: the costs related to contingent liquidity,
or the liquidity buffer that has to be keptto cope with the funding gap risk;
• cs: the credit spread, or the remunerationfor the expected losses for the default ofthe obligor of the asset A;
• op: the cost for the financial and liquid-ity/behavioural options;
• cc: the cost for the economic capital thatis required to cover unexpected credit andmarket risks.
The considerations we have made before aboutthe risk-free rate are valid also for this decompo-sition. All components may typically apply tocontracts with retail or corporate clients, such asmortgages or loans. Some of them do not applyto instruments traded in the market. For ex-ample, a corporate bond rate certainly includesthe risk-free rate ir and the credit spread cs; themarket price usually embeds the assumptionthat the bond is fully financed by equity (i.e.:# = 100%), so that one can either see the creditspread cs including the risk-premium above itshistorical level, or he/she can consider the mar-gin over the risk-free rate as made of the twocomponents: cs and cc. The values of these twocomponents are the equilibrium levels set by theactivity of all the market participants. Fundingspreads can be seen as included in the fu, in theform of the GC (General Collateral) spread overthe risk-free rate ir.
For the Bank’s liabilities, the decompositionis quite simpler, since it may be reduced to thefollowing components:
• ir: the risk-free rate, entering in the thetotal funding cost to pay on liabilities;
• fu: the funding costs due to the spreadspaid over the risk-free rate on liabilities;
Actually, all that matters to the bank is thespread fu paid over the risk-free rate ir: even ifthis margin can be further disentangled in creditand liquidity components, it is always seen asan aggregated cost by the Bank, which can beonly indirectly managed as we have mentionedabove.
After having identified the components ofthe interest rate paid or earned by the Bank, wecan assign each of them to either the IRRBB or
the CSRBB, with the provision that some compo-nents are not included in either one, or: they arenot subject to the measurement and the moni-
3The classification is based on Castagna and Fede [8], Chapter 11. We refer to them for the details on the derivation of thedecomposition of the interest rate we present here.
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FIGURE 2: The components of the rates of assets and liabilities, and their inclusion within the IRRBB or CSRBB frame-
work.
toring of the interest rate or the credit spreadrisk of the banking book, but they can be partof other risk frameworks, such as the liquidityrisk (see Figure 2). We propose to include in theIRRBB framework:
• ir: the risk-free rate;
• op: the cost for the financial and liquid-ity/behavioural options;
We will see that the risk-free rate should be voidof any margin due to credit or liquidity factors,so in theory it should not be a Libor or a Euriborindex. Nonetheless, if the bank chooses to usean index such as the 3M Euribor as a proxy forthe risk-free rate, then all (basis) spreads withrespect to it should be seen as credit relatedfactors, and as such they are part of the CSRBBframework, which includes:
• ir: the risk-free rate;
• fu: the funding costs;
• cs: the credit spread;
for assets, whereas for liabilities cs is not rele-vant. In Figure 2 we show the components forassets and liabilities, and their inclusion in theIRRBB or CSRBB.
The relevant components that we high-lighted for IRBBB and CRSBB purposes enterthe measurement and the monitoring of the riskin two ways, which are strictly related to themetrics the Bank has to compute:
• They can alter the NPV of the financialinstrument or contract, when the metricincludes them (e.g.: the EV, see below):this means that the interest rate i⇤ is partof the contract cash-flows, whose expectedpresent value depends on:
1. the current term structure of the in-terest rates, which determines thediscount factor applied to each cash-flow, and the ir component, if thecoupon is linked to a market indexand periodically repriced, such as thecase of a floating rate bond or mort-gage (usually a spread is added tothe floating component, to be treatedin the CSRBB in case);
2. the (implied) volatility of the interestrates, which affect (together with thelevel of the term structure of the inter-est rates) the value of the financial op-tions embedded in the contract or thesecurity: hence the Bank re-evaluatesthe options’ value whose premiumwas included in the op component;
3. the behavioural options depend onthe level of the rates and other factors,and they affect the amount of the fu-ture expected cash-flows: also in thiscase, the value of the bahvioural op-tionality, whose starting premium inincluded in the op component, is re-evaluated.
• They can alter the future interest rate setfor the replacement of the expiring con-tracts or securities, when this is requiredby the metric (e.g.: the NII, see below): inthis case, all the components included inthe interest rate i⇤ are subject to a repric-ing (not just the floating rates as in thecase above for the NPV); the credit spreadmust be redefined, along with the fundingspread, behavioural options’ value andthe other margins, all contributing to thesetting of the interest rate i⇤ on the newcontract or instrument replacing the ex-pired one.
Our classification differs from the one pro-posed by the BIS document in the Annex 1, butis not totally inconsistent with it: we dare saythat it is only more precise, even though it im-plies a greater efforts from the Bank to set upthe risk measurement and monitoring frame-work. If one wants to adhere to an approachthat is based on our considerations and that issimilar in spirit to that outlined by BIS, thenthe following term structures, with the relatedshock scenarios, are needed for each currency:
• A risk-free rate curve, which is exactly thesame as that prescribed by the document[3];
• A number of basis curves, representingthe spread of the indices to be monitored(e.g.: 1M Euribor, 3M Euribor, etc.) overthe risk free curve.
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• A number of credit spread curves, rep-resenting the spread over the risk-freecurve or over the reference index curve(e.g.: 6M Euribor) remunerating the creditrisk: these curves can be designed forcountries, economic sectors and type ofobligors, of for single names. Moreover,they can be further separated in two setsof terms structures, one for the generalmarket credit spread and another for theidiosyncratic credit spread.
• A number of funding spread curves, repre-senting the spread over the risk-free curveor over the reference index curve (e.g.: 3MEuribor), paid by the bank on the differentfunding sources included in the liabilities:these curves embed the entire spread, andnot just the component due to the creditrisk as in the case of the credit spreadcurves.
For each of these curve shock scenarios mustbe designed in order to assess the impact on therisk metrics. As discussed above, no generalrules or indication are provided in the BIS doc-ument [3]; we like to stress here just a coupleof points, referring to a separate research a de-tailed analysis:
• The number of scenarios for each of theadditional curves should be in line withthe number of scenarios set for the risk-free curves: this allows for joint scenariosthat include the correlation between thesingle basis, credit, funding componentsand the risk-free rates.
• For the basis curves, scenarios should def-initely be designed relying on a robustbasis model linking together the spreadson the different indices: one of such frame-works is in Castagna et al. [7].
• The resulting curves can be used to buildup the new interest rate i⇤ for the con-tracts rolling over the expired potions, asfor NII purposes. Additionally, PDs haveto be extracted from the curve, to calculatethe expected present value of the futurecash-flows, both for NII and EV valuespurposes (we will have a more in depthdiscussion on this point below).
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FIGURE 3: The IRRBB framework.
The IRRBB Framework
The general IRRBB framework is outlined inthe Principles’ section of the Basel document:Figure 3 shows a schematic overview of theframework.
The ultimate responsibility is attributed tothe Government Body of the Bank, that musthave the global oversight on the IRRBB Man-agement and Measurement, checking also thecompliance with the Risk Appetite Frameworkof the Bank. There are two areas that are in-cluded within the IRRBB framework: the man-agement and the measurement of the relevantrisks. These tasks are typically delegated tomore technical functions of the Bank, whereskills and in depth knowledge reside. The man-agement of the IRRBB is generally assigned toan Asset Liability Committee (ALCO), whereasthe measurement of the IRRBB is operatedwithin the Risk Department.
The organisation of the activities from thesetting of appropriate limits, including the defi-nition of specific procedures and approvals nec-essary for exceptions; to the monitoring andthe compliance with those limits; the set-up ofadequate systems and standards for measuringthe risks, valuing positions and assessing per-formance; the design of procedures to updateinterest rate shocks and stress scenarios; the pro-duction of a comprehensive IRRBB reporting;the creation of a review process and effectiveinternal controls and management informationsystems (MIS).
The activities run by the ALCO, within theIRRBB management scope, should be compliantwith the policies and procedures for limitingand controlling the IRRBB, and in any case notexceeding the powers delegated by the Govern-ment Body. The risk is managed by means ofauthorised instruments, hedging strategies andrisk-taking opportunities. All IRRBB policiesshould be reviewed periodically (at least annu-ally) and revised as needed, according to theBasel document.
The measurement of the IRRBB, operated bythe Risk Department, is based on the results ofboth economic value (EV) and earnings-based(NII) measures. These are produced by meansof a wide and appropriate range of interest rateshock and stress scenarios, with a minimum
compulsory set of them defined by the Baseldocument.
Other guidelines are provided regarding thebehavioural and modelling assumptions (Princi-ple 5, see below for a more in depth discussion);the accuracy of data, the documentation andthe testing and the validation of models (Prin-ciple 6); the internal reporting and the externaldisclosure on the IRRBB levels and the internalprocedures implemented to manage the relevantrisks (Principle 7 and 8).
The IRRBB framework, once the risks havebeen duly managed and/or measured, leadsto the Bank’s internal assessment of the capitalthat is considered adequate to cope with theresidual risks. The Principle 9 of the Basel doc-ument indicates that the Bank should embedthe assessment of the capital adequacy for theIRRBB within the ICAAP, considering also therisk appetite set in the RAF. There are no spe-cific minimum requirements, but the genericprovision that the overall level of capital shouldbe commensurate with both the Bank’s actualmeasured level of risk (including for IRRBB)and its risk appetite, and be duly documentedin its ICAAP report. The document “clarifies”the following:
• the capital will cover the risks measuredby the EV metric;
• for the NII metric, the Bank will consideronly a capital buffer.
The difference between the capital adequacy tocope with risks related to the EV, and the capi-tal buffer referring to the NII, should be simplydisregarded, in our opinion, since in any casethe Bank should provide for enough capital toboth cover the economic value and the earnings’volatility.
Additionally, Principle 9 lists a set of factorscontributing to the capital assessment for theIRRBB, running from the size of the exposureof the internal limits; to the sensitivity of themeasures to key assumptions; to the impact ofembedded losses; to the drivers of the underly-ing risks.
The most important indication of Principle9 is perhaps that Banks should not only relyon supervisory assessments of capital adequacyfor IRRBB, likely by means of the standardisedapproach outlined in the document, but they
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should also develop their own methodologiesfor capital allocation, based on their risk ap-petite. So, there is a strong incentive to workon proprietary methodologies to measure theIRBBB.
Anyhow, the lack of any specific minimumrequirement for the IRRBB risk has to be con-nected with the principles guiding the Supervi-sors, which we quickly analyse right below.
Actually, the last three Principles are meantto steer the Supervisors: they have to collect,on a regular basis, all needed information tomonitor trends in banks’ IRRBB exposures, as-sess the soundness of banks’ IRRBB manage-ment and identify outlier banks that should besubject to review and/or should be expectedto hold additional regulatory capital (Principle10). Additionally, Supervisors should regularlyassess banks’ IRRBB frameworks and evaluatethe effectiveness of the approaches that banksuse to identify, measure, monitor the relevantrisks; to this end Supervisors should employspecialist resources, considering the complexityof the task (Principle 11). Finally, Supervisorsmust publish their criteria for identifying outlierbanks, which should be considered as poten-tially having problems with IRRBB exposures.When a review of a bank’s IRRBB exposure re-veals inadequate management or excessive risksrelative to capital, earnings or general risk pro-file, Supervisors must require mitigation actionsand/or additional capital (Principle 12).
The criteria to identify outlier banks can befreely chosen by Competent Supervisory Au-thorities, but the Basel document (see par. 88,[3]) prescribes at least one materiality test:
• the ratio of the maximum variation of theEV, calculated in the six mandatory sce-narios,4 to the Tier 1 Capital. When theratio is above 15%, and in any case whenthe Supervisors deem that the IRRBB isundue, a set of actions can be requestedto the Bank, including the reduction of itsIRRBB exposures, additional capital, con-straints on the internal risk parameters,and improvement of the risk managementframework.
Additional outlier/materiality tests can be pre-scribed by the Supervisors, but in any case thethreshold for defining an outlier bank shouldbe at least as stringent as 15% of Tier 1 capital.
Interest Rate Shocks and Stress Scenarios
Banks need internal systems flexible enough tocalculate the risk metrics (economic value andnet interest income) in a wide range of scenarios.The BIS document [3] cites:
• internally selected interest rate shock sce-narios addressing the bank’s risk profile,according to its ICAAP;
• historical and hypothetical interest ratestress scenarios, more severe than shockscenarios;
• the six prescribed interest rate shock sce-narios detailed in Annex 2 of BIS [3];
• any additional interest rate shock scenar-ios required by supervisors.
The selection of relevant shock and stress sce-narios will likely require the involvement of sev-eral experts from different departments withinthe Bank, such as traders, the treasury depart-ment, the finance department, the ALCO, therisk management and risk control departmentsand/or the Bank’s economists. The opinion ofall these experts should be taken into accountwhen designing a stress-testing programme forIRRBB.
Additionally, the BIS document provides thefollowing guidelines:
• the scenarios should identify parallel andnon-parallel gap risk, basis risk and op-tion risk. The scenarios are both severeand plausible, in light of the existing levelof interest rates and the interest rate cycle;
• special consideration should be given tocontracts or markets where the Bank has aconcentration risk, due to a more difficultliquidation a stressed market conditions;
• interaction of IRRBB with its related risks(e.g.: credit risk, liquidity risk, etc.) shouldbe accounted for;
• adverse changes in the spreads of newassets/liabilities replacing maturing as-sets/liabilities over the horizon of theforecast of NII: this means that scenariosare needed also for credit and fundingspreads;
• significant option risk should be ad-dressed with scenarios including the ex-ercise of such options (e.g.: sold caps and
4The six mandatory scenarios are outlined in the Annex 2 of the Basel document [3].
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floors) affect the risk positions when theybecome in-the-money. The Bank shouldalso make assumptions to measure theirIRRBB exposures to changes in interestrate volatilities;
• the Bank has to specify the term structureof interest rates used in the scenarios (e.g.:the EONIA swap curve) and the basis rela-tionship between yield curves, rate indicesetc. (e.g.: the basis between the 3M Euriborcurve and the EONIA swap curve). Wheninterest rates are administered or man-aged by management (e.g.: prime rates orretail deposit rates), assumptions on theirsetting have to be clearly documented.
Formally, we define a term structure ofinterest rates as a collection of interest rates{R(t1), R(t2), ..., R(tN)}, each of them associ-ated with a maturity belonging to the set chosenby the Bank (or indicated by the BIS document[3] for the standardised approach) {t1, t2, ..., tK}:
T R = {[R(t1), t1], [R(t2), t2], ..., [R(tK), tK]}(2)
Firstly, we need to precisely define whichkind of rate R(tk) represents. According to theBIS document [3], it has to be a risk-free rate,so we think that the best choice is to derive therates implied in the EONIA swap curve tradedin the market. The EONIA rate are the best ap-proximation to a risk-free rate, since it embedsthe credit risk for a ond-day loan in the inter-bank market. Swaps whose underlying floatingrate is the EONIA, if fully collateralised (as it isthe case when traded in the interbank market),allow to derive EONIA rate for longer matu-rities, still preserving the minimum one-daycredit risk spread. Secondly, at the referencedate t0, we extract from EONIA swaps’ mar-ket quotes the zero-interest rates R(tk) for anyexpiry date tk.
The scenario should be applied to these zerorates. Each scenario can defined as a set ofshocks referring to each expiry tk, or formally:
J R = {[JR(t1), t1], [JR(t2), t2], ..., [JR(tK), tK]}(3)
So, the resulting curve for a given scenario J R
is:
T RJ R ={[R(t1) + JR(t1), t1], [R(t2) + JR(t2), t2],
, ..., [R(tK) + JR(tK), tK]}(4)
where each element of the set can be denotedas RJ R(tk) = R(tk) + JR(tk).
For CSRBB purposes, we have sketched inSection 1 an extended framework with addi-tional curves, to take into account the basis andthe credit factors embedded in the rates paidand earned by the Bank. For these curves, asimilar formal definition can be set up. For ex-ample, a basis curve, e.g.: 3M Eurbor - 3M Eoniaspread, is formally built as a collection of basisspreads {B(t1), B(t2), ..., B(tN)}, each of themassociated with a maturities {t1, t2, ..., tK}:
T B = {[B(t1), t1], [B(t2), t2], ..., [B(tK), tK]} (5)
Each scenario for the basis is defined as a set ofshocks referring to each expiry tk, as above:
J B = {[JB(t1), t1], [JB(t2), t2], ..., [JB(tK), tK]}(6)
and the resulting basis curve for the scenarioJ B is:
T BJ B ={[B(t1) + JB(t1), t1], [B(t2) + JB(t2), t2],
, ..., [B(tK) + JB(tK), tK]}(7)
and each element of the set can be denoted asBJ B(tk) = B(tk) + JB(tk).
Similarly, we can formally define startingand shocked credit curves, T C and T C
J C .
Behavioural and Modelling Assumptions
Behavioural and modelling assumptions are cru-cial to determine the sensitivity of both the EVand the NII, since many contracts in the balancesheet have these type of optionalities embed-ded. We have already mentioned that Principle5 provides some guidance for the behaviouralmodelling, specifically referring to the followingtype of contracts’ features:
• the volume and the interest of the non-maturing deposits (NMD);
• the amount of withdrawals of credit linesand the value of the credit spread optionsold to the debtor by the bank;
• prepayment of fixed (or floating) rateloans;
• fixed rate commitment, whereby the Bankoffers its customers to draw a loan at apredetermined rate for a period of time;
• expectations for the exercise of interestrate options (either explicit or embedded)by both the Bank and the customers, e.g.:
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options embedded in callable or puttablebonds issued by the Bank;
The Bank can design its own frameworksto deal with behavioural features of the con-tracts. In this case, the Bank should make con-ceptually sound and reasonable modelling as-sumptions, which agree with with historicalexperience. Moreover, the behaviour should notonly be dependent on the interest rates, but alsoon other factors that reasonably may affect thecounterparty.
The BIS document [3] prescribes that banksmust carefully consider how the exercise of thebehavioural optionality will vary not only un-der the interest rate shock and stress scenariobut also across other dimensions. Principle 5lists possible additional factors, distinctly foreach type of contract: they include geographi-cal location, remaining maturity, loan-to value(for prepayment of mortgages and fixed rateloan commitments); depositors characteristics,competitive environment, GDP, unemploymentand other macroeconomic variables (for non-maturing and term deposits).
We will dwell more on the behavioral mod-elling below, and we will flesh out the subtletiesimplied in the standardised approach.
Measuring the IRRBB Risk
As mentioned above, the Principle 4 establishesthe two pillars of the IRRBB measurement, viz.the outcomes of both EV and NII metrics. Be-fore analysing the new standards, we define informal terms the two metrics and establish therelationship existing between them.
Formal Definitions of the Economic Value andthe Net Interest Income
Let {d1, d2, ..., dN} be the set of contracts that fallwithin the definition of interest-rate sensitive as-sets, existing within the Bank’s balance sheet atthe reference date t0; let TE be the terminal dateconsidered in the calculation of the EconomicValue. Each contract can be defined as a set ofpossibly stochastic cash-flows, occurring at pre-defined dates indicated as ti, with i = 1, 2, ..., IEand tIE = TE.
The Economic Value (of the Equity) is de-fined as the net expected discounted cash-flowsof all the contracts up to the terminal date TE,
corresponding to the last payment of the longestcontract in the Bank’s balance sheet. As per thedefinition, the contracts are those in the assetsand in the liabilities of the balance sheet. Informula, we have:
EV = E N
Ân=1
IE
Âi=0
D(t0, ti)cf(t0, ti; dn)
�(8)
where D(t0, ti) is discount factor for time ti,cf(t0, ti; dn) is the cash-flow occurring in ti forthe contract dn calculated at the reference timet0. If we indicate cf(t0, ti; dn) = Ân cf(t0, ti; dn),then we can rewrite (8) in a more compact formas:
EV = E IE
Âi=0
D(t0, ti)cf(t0, ti)
�(9)
The Economic Value can be seen as the ex-pected present value of the Bank’s assets, net ofthe Bank’s liabilities. The metric is the algebraicsum of the NPVs of the assets and the liabilitiesat the assumed liquidation (or closing) price onthe market. As such, the Economic Value of theEquity cannot be considered as the net valueof the Bank, seen as a firm. In Castagna [6] wediscussed how each contract should be valuedwhen entering in the Bank’s balance sheet, if theBank wishes to assess its own value (which isthe same as saying: the value to the sharehold-ers): this type of evaluation is not the liquida-tion value of the contract, but it considers theBank as bundle of contracts that imply subjec-tive5 credit and funding adjustments, includingthe overall adjustment (referring generically toall contracts) due to the limited liability that theshareholders are granted with, which we nameLimited Liability Value Adjustment (LLVA).
To stress the view of the EconomicValue as the sum of the NPVs of all con-tracts existing at the reference date t0, letVn(t0, Td) = E[Âi D(t0, ti)cf(t0, ti; dn)] be the ex-pected present value of the cash-flows of con-tract n expiring in Td. Then:
EV =N
Ân=1
Vn(t0, Td) (10)
For risk management purposes, what is im-portant is the variability of the EV. There aremany ways to measure the variability: the onethe Basel document [3] chooses is the variationof the Economic Value due to a change of theterm structure of the interest rates accordingto a predefined set of scenarios. Let Ds(t0, ti)
5“Subjective” should be meant as “specifically referring to the Bank”.
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and cfs(t0, ti) indicate, respectively, the discountfactors and the cash-flows associated to a givenscenario s: a scenario is a modifier of the termstructure of the (risk-free) interest rates at thereference date t0. A modification of the termstructure of interest rates affects both the dis-count factors and all the cash-flows that dependon the market rates, e.g.: the coupons of float-ing rate assets. The EV corresponding to thescenario s is:
EVs = E IE
Âi=0
Ds(t0, ti)cfs(t0, ti)
�
So we define the variation of the EV in scenarios as: DsEV = EVs � EV.
The Net Interest Income is defined a the sumof cash-flows occurring from up to a given short-term horizon TNII , so that typically TNII < TE.This definition is found in most standard textbook dealing with ALM, although it is in manycases it is not explicitly stated if the cash-flowsshould be discounted or not.6
The definition of the NII without discount-ing seems to be more in line with the definitionin the Basel document [3], but in the previousBIS consultative paper [2], the definition of theNII, and the formula to compute its sensitivity,explicitly included the discounting, so it is notclear whether to discount or not the cash-flows.
Additionally, the document [3] states thatthe NII is computed under the assumptionof a constant balance sheet, i.e.: all the ex-piring contracts are replaced by a new oneexactly similar to old one. For this rea-son, let us define the extended set of con-tracts {d1, d2, ..., dN , dN+1, ..., dM}, where thecontracts dN+1, ..., dM replace the expiring onesin {d1, d2, ..., dN} within the horizon TNII . As-sume now that the last date included in thecalculation is tI = TNII .7 We define in formalterms the NII as:
NII = E M
Âm=1
INII
Âi=0
cf(t0, ti; dm)
�(11)
where tINII = TNII . Once again, settingcf(t0, ti; dn) = Âm cf(t0, ti; dm), equation (11) be-
comes:
NII = E INII
Âi=0
cf(t0, ti)
�(12)
Also for the NII, for risk-management pur-poses, we define the variation of the NII, whichsimilarly to the EV is DsNII = NIIs � NII,where the notation referring to the scenariois the same as in the EV case. So DsNII =NIIs � NII is given by the differences in pro-jected future cash-flows due to the a scenarios in which a different interest rate term struc-ture than the market one at the reference dateis used:
NIIs = E M
Âm=1
INII
Âi=0
cfs(t0, ti; dm)
�
It is worth stressing that the cash-flows in-cluded in the NII, up to horizon TNII , do notclash with the cash-flows included in the cal-culation of EV,8 since new contracts may beadded due to the possible expiry of some of then contracts existing at t0.
Fact 1 In case the NII is computed with discountedcash-flows, without the constant balance sheet as-sumption and up to the final date of the longestmaturity contract, it will coincides with the EV.
Similarities and Differences between the EVand the NII
We would like to understand which is the infor-mation content conveyed by the EV and the NII,and their sensitivity to distinct scenarios. Morespecifically, we would like to understand if theyactually provide different indications about therisk the Bank bears, and to which extent theydo so. On the other hand, we would to identifyif the two metrics qualitatively agree in identify-ing a given risk profile the Bank has at a certainpoint.
For comparison purposes, we will computeboth the EV and the NII until the expiry of thelongest maturity contract, so that TNII = TE =10 years after the reference date t0.
In our opinion, the best way to investigatethe similarities and the differences between the
6The reader may refer to Bessis [4], and Choudry [10] and [11], to mention only a couple of examples of relatively recentbooks on ALM. In both these books, the authors focus more on the DNII, which we defined just below, so that they deal withthe gap of sensitive contracts on different maturities, rather than sum of cash-flows. This is simply another way to see theNII.
7The constant balance sheet assumption is typically not considered in text books on ALM.8We clearly refer to the cash-flows in the calculation of EV for the sub-period [t0, TNII ], which is included in the whole
period [t0, TE].
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Base Scenario +200bps ScenarioExpiry DF Zero Rates 1Y Rates DF Zero Rates 1Y Rates
0 1.000000 0.65% 1.000000 0.65%1 0.993550 0.65% 1.35% 0.973877 2.65% 3.39%2 0.980348 0.99% 1.91% 0.941908 2.99% 3.97%3 0.961979 1.29% 2.36% 0.905958 3.29% 4.43%4 0.939812 1.55% 2.71% 0.867556 3.55% 4.79%5 0.914974 1.78% 2.99% 0.827902 3.78% 5.08%6 0.888370 1.97% 3.21% 0.787913 3.97% 5.30%7 0.860706 2.14% 3.39% 0.748262 4.14% 5.47%8 0.832525 2.29% 3.52% 0.709431 4.29% 5.61%9 0.804232 2.42% 3.62% 0.671751 4.42% 5.71%
10 0.776128 2.53% 3.70% 0.635440 4.53% 5.80%11 0.748429 2.63% 3.76% 0.600628 4.63% 5.86%12 0.721289 2.72% 3.81% 0.567386 4.72% 5.91%13 0.694814 2.80% 3.85% 0.535738 4.80% 5.94%14 0.669074 2.87% 3.88% 0.505675 4.87% 5.97%15 0.644112 2.93% 3.90% 0.477170 4.93% 6.00%16 0.619950 2.99% 3.91% 0.450176 4.99% 6.01%17 0.596599 3.04% 3.93% 0.424641 5.04% 6.03%18 0.574055 3.08% 3.94% 0.400505 5.08% 6.04%19 0.552310 3.12% 3.94% 0.377704 5.12% 6.04%20 0.531350 3.16% 3.95% 0.356174 5.16% 6.04%
TABLE 2: Eonia discount factors and curves for zero rates and forward 1Y rate indices, for maturities 1 year to 20 years.
Base scenario (market at reference date) and “200bps Up” Scenario.
EV and NII is through a practical, if stylised,example. To this end, let us consider a set ofOIS curves at time t0 for a given currency, sayEuro, which are shown in Table 2. To get atthe heart of the matter, without complicatingtoo much the analysis, we assume that no ba-sis exits between Eonia and Euribor rates, sothat the term structure of Eonia fixings, e.g.: 1Y,do not differ from the corresponding curve of
Euribor fixing. Basically, we are neglecting thebasis risk that in reality exists. In terms of thenotation introduced in Section 2, we have theJ R = {[+2%, 1Y], [+2%, 2Y], ..., [+2%, 20Y]}.
In Table 2 we show the Eonia discount fac-tors and zero rates, and the forward 1Y rate, forthe base scenario at the reference date t0, andfor a scenario where the Eonia zero rate curveis bumped +200 bps up at each tenor.
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Assume now that the Bank has a very simpli-fied balance sheet made of one asset, starting attime t0, paying an annual coupon and expiringin 10 years, which is funded by one liabilityexpiring in 5 years, paying an annual coupontoo. Assume also, rather unrealistically, thatthe equity is nil. The bank does not pay anyfunding spread over the Eonia curve, and theasset has no credit risk, so that it can be pricedwithout any adjustment for credit losses. Boththe asset and the liability are fairly priced giventhe Eonia curve, so that they are both worth1,000,000.00 at inception; additionally, the mar-ket fair coupon for the asset is 2.5006%, whereasit is 1.7748% for the liability. The Bank’s balancesheet, marked to the market, at t0 reads as:
Assets LiabilitiesA1 = 1, 000, 000.00 L1 = 1, 000, 000.00
——————–E = 0.00
The EV is the sum of the cash-flows of twocontracts, as shown below:
Asset LiabilityInterest Capital Interest Capital
25,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.37 1,000,000.0025,006.3125,006.3125,006.3125,006.3125,006.31 1,000,000.00
The NPV of both the asset and the liabilityis 1,000,000.00, with opposite signs, so EV = 0.Assume now we apply the “+200bps Up” sce-nario, which we define s = PU: the new dis-count factors, zero and forward 1-year ratesare shown in Table 2, and we have the newEVPU = �70, 834.59. This is the result of achange of the NPV of both the asset and theliability:
NPVAsset 837,240.66Liability 908,075.24Net - 70,834.59
So DPUEV = �70, 834.59. What can be in-ferred from the negative sensitivity to a parallelupward shift of the interest rate curve is thatcontracts that are affected negatively by interestrates’ raise, typically assets, have longer matu-rity than contracts that are positively affectedby the same raise, typically liabilities.
Let us now examine the NII: we have toinclude also the cash-flows originated by thestatic balance-sheet assumption. In this case, we
have to replace, after 5 years, the maturing lia-bility with one of similar features, which meansthat the bank will issue a 5-year fixed rate bond,whose coupon can be deduced from the interestrate curve at the reference date. The impliedcoupon for a 5-year bond in 5 years is 3.3361%,so that the cash-flows we have to consider are:
Asset LiabilityInterest Capital Interest Capital
25,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.37 ± 1,000,000.0025,006.31 33,360.6225,006.31 33,360.6225,006.31 33,360.6225,006.31 33,360.6225,006.31 1,000,000.00 33,360.62 1,000,000.00
The ± sign in the “Capital” cash-flows of theliability side means that 1 million is reimbursedon the expiring debt and then received back bythe bank on the issuance of the new debt. Atthe reference date NII = �5, 481.87.
In the scenario UP, the shift upwards of theinterest rate term structure implies a higher for-ward 5-year rate in five years, which will beequal to 5.3298%. The new implied forwardrate will alter the future cash-flows as follows:
Asset LiabilityInterest Capital Interest Capital
25,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.3725,006.31 17,748.37 ±1,000,000.0025,006.31 54,172.1025,006.31 54,172.1025,006.31 54,172.1025,006.31 54,172.1025,006.31 1,000,000.00 54,172.10 1,000,000.00
so that NIIPU = �109, 539.25. The variationof the NII, DPUNII = �104, 057.38.
Comparing the two metrics, it seems thatthe Bank has a higher sensitivity for the NIIthan the EV, in the scenario PU. In reality, thisdifference is due to the discounting of cash-flows, which is missing the NII metric. Actu-ally, if we consider a discounted NII, whereall the cash-flows are discounted at the refer-ence date, we have that NII = 0.00 and, inthe scenario PU, NIIPU = �70, 834.59, so thatDPUNII = �70, 834.59, which is exactly the sen-sitivity of the EVPU to the same scenario.
The negative sensitivity of the NII, either dis-counted or un-discounted, is subtler to interpret.Actually, since the metric is computed under theconstant balance sheet assumption, the assets’
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maturity will be matched by the liabilities’ matu-rity, even though the negative sensitivity signalsa roll-over, or repricing, of contracts whose NPVis positively affected by a general increase of theinterest rates, typically liabilities.
From the analysis above, we can draw thefollowing conclusion:
Fact 2 When accounting for the discounting, andsetting an identical time horizon for both, the NIIand the EV show an equal sensitivity to a givenscenario, so that they are not only qualitatively, butalso quantitatively equivalent. This is true even ifthe NII is computed under a constant balance sheetassumption, provided we are in an economy wherecredit risk does not exist, so that no credit or fundingspreads are included in the interest rate of assets orliabilities.
The fact that the Basel document refers toan un-discounted NII is likely due to the factthat its variations have to be monitored, and re-ported, in relation to a projected period of onlyone year, whereas the EV and its variations haveto consider the entire life of all the instrumentsincluded in the balance-sheet at time t0.
It is worthwhile to investigate what happensif the bank tries to immunise the sensitivity ofthe two metrics against a given scenario. Let usassume again that the scenario is the PU consid-ered above, and that the Bank wants to hedgethe EV. To this end, the Bank may recognisethat in the EV calculation the renewal of ex-piring liability in five years is totally neglected.Nonetheless, in five years the current balancesheet shows there will not be enough liquidityto pay back the bond, so the bond must be rolledover for another period of five years, when thematuring asset will provide the liquidity neededto pay the liability.
Since this transaction is quite sure to hap-pen,9 the Bank decides to lock in the cost atthe current market conditions, by entering ina 5Y5Y payer swap. That means that the Bankenters in a swap staring forward in five years,maturing in five years after the start, in which itwill pay a fix rate against receiving a 1Y Euribor,on an yearly basis.10 The notional amount is thesame as the liability, i.e.: 1, 000, 000.00.
From the interest rate term structure at thereference date t0, the fair 5Y5Y swap rate is3.3361%, which is naturally the same as the im-plied forward par rate on a fixed rate bond start-ing in five years and maturing after five more
years (we have calculated it to determine thecash-flows in the NII). In five years the Bankcan issue a new bond maturing in five years,with a floating 1-year coupon, which will benetted out by the floating rate received on theswap, and it will be left only with a net paymentequal to fixed rate of the swap of 3.3361%, on1, 000, 000.00. The total cash flows will be thesame as in the base scenario case for the NIIshown above.
We have also in this case that EV = 0, be-cause the swap contract has zero value at incep-tion. When computing the EV in the scenarioPU, we have that EVPU = 3, 104.37, as shownbelow:
Asset 837,240.66Liability 908,075.24Swap 73,938.96Net 3,104.37
so that DPUEV = 3, 104.37. The hedgeworked out quite fine, since in the un-hedgedcase the DPU was �70, 834.59: the residual vari-ation of 3, 104.37 is due to the convexity of theasset and liability, which was not hedged.
In conclusion, when considering a constantbalance sheet also for the EV calculations, andhedging the sources of volatility with marketinstruments (a swap in our case), right fromthe reference date, the variations of the EV aredramatically reduced.
Let us see what happens if we consider thesame hedge for the NII: we need to include inthe cash-flows those originated by a bond thatrolls over the maturing liability in five years.This will be a fixed rate bond, to comply withthe requirement that the replacing contractsmust have the same features as the expiringones. When issuing this new bond in five years,the Bank will trade a swap in which it will paythe floating rate and receive the fixed rate. Thefloating rate payment will be netted out by thefloating rate received on the 5Y5Y swap tradedin t0; the fixed rate received on the new swapwill net out the fixed rate paid on the new is-sued bond (the two rates will be identical bydefinition), so that the total net payment will bethe fixed rate paid in the 5Y5Y swap, of 3.3361%,on 1, 000, 000.00. Figure 4 shows the diagram ofall the in and out cash-flows, with the net totalresulting cash-flow, referring to the interest ratepayments.
9At least on a going-concern basis, the renewal of the liability is certain.10The payment schedule is not exactly the market standard in the Euro, but such a swap is definitely tradeable in the
interbank market.
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FIGURE 4: Interest rate payments on the new bond issued by the bank and on the 5-year swap traded in the fifth year,
along with the payments on the 5Y5Y swap traded on the reference date, and the final total net cash-flow.
It is easy to check that one again, the to-tal cash-flows will be the same as in the basescenario for the NII shown above, both in thebase and in the PU scenarios. When discount-ing the NII, to compare its to the DEV, wehave that NII = 0.00 NIIPU = 3, 104.37, sothat DNIIPU = 3, 104.37, which is the same asDEVPU for the hedged case.
Fact 3 If we hedge against a given scenario eitherthe EV or the NII, we are hedging also the other; thehedged sensitivity to the shocked scenario is the samefor both metrics.
It should be stressed that all that we haveshown is valid only
• for the discounted cash-flow NII;
• under a constant balance sheet assump-tion;
• if the calculation is operated for the sametime horizon as for the EV.
Banks do not compute the two metrics in thisway though, and also the Basel document [3]prescribes a different rule for them, since theNII is calculated only for a one-year horizonand with un-discounted cash-flows. It is then
most likely that the variability of the two met-rics cannot be hedged simultaneously and theBank should focus on one of them.
Cash-flow Profiles, Dividends and Risk-Measurement
There is also another possibly risky practicaloccurrence to analyse, which can, or cannot, bedetected by the EV and the NII: the cash-flowprofile. We saw that in the base scenario, at thereference date, both the EV and the discounted,constant balance sheet NII have zero value, ba-sically providing an indication of the fairness ofthe values of the asset and the liability. Whatwas not taken into account is that the Bank willassess its profits and losses (P&L) at the end ofevery year, and it will be mostly done (at leastfor the part concerning the interests) on a cash-flow basis by measuring the net income as thedifference between interests received and paidduring the past year.
It is when yearly P&L is assessed, and basedon it dividend are paid, that the cash-flowschedule can play a role: at the reference date,the income is fairly balanced by the cost, asshown by the zero value of the two metrics.That means that positive cash-flows will be, onan present value basis, exactly compensated
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by negative ones. The same balance is alsoachieved if one does not consider the presentvalue, but looks at the cash-flows that are rein-vested until the terminal date of the calculation,10 years in our example. To see this, we showthe cumulative cash-flows, reinvested at theforward rates each year (capital cash-flows areomitted since the net out to zero any time theyoccur):
InterestAsset Liability Year NII Cumul. Cash-Flows
25,006.31 17,748.37 7,257.94 7,355.6825,006.31 17,748.37 7,257.94 14,892.6525,006.31 17,748.37 7,257.94 22,673.0725,006.31 17,748.37 7,257.94 30,743.5225,006.31 17,748.37 7,257.94 39,139.4925,006.31 33,360.62 - 8,354.31 31,774.6125,006.31 33,360.62 - 8,354.31 24,213.0825,006.31 33,360.62 - 8,354.31 16,416.6825,006.31 33,360.62 - 8,354.31 8,354.3125,006.31 33,360.62 - 8,354.31 - 0.00000
In the last column, we see that if the Bankreinvests on a yearly basis the yearly NII, it willachieve a nil balance at the end of the calcu-lation period, exactly as the nil present value.We have considered all the cash-flows impliedby the constant balance sheet assumption, sothat also those originated by the roll-over of theliability are included.
The problem is that the Bank will mark aprofit, and likely distribute a dividend, everyyear producing a positive partial NII. So, forthe first five years, it will distribute yearly div-idends equal to circa 7, 258, while it will marka yearly loss of circa 8, 354.31 for the next fiveyears. In practice, the Bank will not be accu-mulating sufficient funds to cover the negativecash-flows of the years six to 10.
This behaviour is perfectly legitimate undera civil law point of view, since accounting princi-ples allow to determine the P&L exactly how wedescribed. Nonetheless, the Bank knows fromthe start that, under a financial point of view,this policy will eventually bring to the default,or at least to a call for an equity increase fromshareholders, which means in practice to takeback the distributed dividends.
It is worth stressing that the cash-flow pro-file is deterministically given by the contractsexisting at the reference date, whereas they areprojected according to the implied forward ratesfor the rolled over liability. We saw before thatthis forward rates can be locked in at the refer-ence date by entering in payer 5Y5Y swap, sothat the entire cash-flow schedule becomes fixed.
If the Bank prefers not to hedge the repricingin 5 years, then it may expose itself to a riskthat may lead to a greater loss, in case of shiftupward of the interest rate term structure abovethe implied forward rates, or a lower loss oreven a profit of the interest rates move down-ward.
We may also add that, disregarding the ef-fects due to the new production, the positiveNII generated by the banks are generally pro-duced by the maturity transformation activ-ity, similar to the stylised balance-sheet we areworking in. By maturity transformation wemean the un-hedged funding of longer maturityassets with shorter maturity liabilities.
Assuming that the bank has hedged itsrepricing exposure in 5 years, to eliminate onesource of uncertainty from the analysis, we sawabove that both the EV and the discounted NIIhave the same negligible sensitivity to interestrate movements. So, both metric would not im-mediately signal a potential harmful situationto the Bank.
To identify the possible risks related to thematurity transformation, one possible solutionis monitoring the partial yearly (discounted orun-discounted) NII: the third column of the ta-ble above is the tool to detect the evolution ofthe cash-flow schedule. It is not clear, though,what that Bank should do once a dangerous con-dition has been identified. Actually, the Bankhas already hedged its exposure to interest raterisk, so the future losses are arising only fromthe accounting standard that allow to distributedividends by measuring the P&L of the interestrate income on a cash-flow basis.
Additionally, technically speaking, since the5Y5Y swap is not hedging an existing contract, ithas to be marked to the market yearly11, and thevariation of the NPV contributes to the yearlyP&L of the Bank. So, when interest rates raise,and subsequently also the NPV of the 5Y5Yswap increases, the Bank would be distribut-ing even more dividends, thus worsening theeffectiveness of the hedge.
The only solution that seems to be soundfrom a financial point of view, and that allowsthe Bank to follow the accounting principles toassess the yearly P&L, is a different hedgingpolicy that relies on transforming all the assetsand the liabilities from fixed to floating rate,if necessary, right from the reference date. Inmore details, the Bank should swap its assets
11According to accounting principles, it cannot be treated on a hedge-account basis, so that it has to be marked to themarket.
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FIGURE 5: Interest rate payments on the bonds issued at the reference date and after 5 years, along with the payments on
the asset and of the two swaps from fix to floating rate for both of them, and the final total net cash-flow.
from fix rate to floating rate (in our stylisedbalance sheet, a 1Y floating rate); at the sametime, it should swap all the liabilities from fixto floating rate (again, 1Y floating rate in ourexample).
By swapping both assets and liabilities, theinterest rate net income is nil, since the two float-ing rate interests on the asset and the liabilitywill be zeroing out each other. Moreover, after5 years, the roll over of the maturing liabilitycan be operated by issuing a new floating rate5 year bond, still preserving the netting to zeroof the received and paid interests. There is noneed to hedge the repricing with a 5Y5Y swap,since any market level of interest rates will bematched by the floating rate received on the as-set. Figure 5 shows all the cash-flows involvedin the hedging we have just outlined.
Moreover, the EV and the NII sensitivitieswill be almost zero, since all the assets and liabil-ities are indexed to short term (1 year) floatingrates.
The policy to swap every fixed rate contractto a floating rate contract will eliminate anyfalse profit due to the maturity transformation
activity, and the Bank will not distribute anydividend for mis-accounted profits. The onlynet interest income will derive from the abilityof the Bank to charge a margin over the mar-ket interest rates, in addition to all the marginsthat are covering expected losses (i.e.: the creditspread), the funding costs (i.e.: the cost of fund-ing spread), embedded or financial optionalities,and infrastructure costs. In conclusion, from allthe analysis we presented, we can derive thefollowing general rule:
Fact 4 Due to the different assessment of the yearlyprofits made by financial and accounting principles,the only sound policy that allows:
• to reduce to zero the sensitivity to interestrates’ movements of both the EV and the NII;
• to avoid distributing wrongly computed divi-dends,
is dealing only in short term floating rate contractsboth for assets and liabilities. In case this is notpossible, whenever a fixed rate contract is closed, itshould be immediatley swapped to floating rate.
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FIGURE 6: Interest rate payments paid and received, and their total, when the equity is modelled as a 10-year maturing
fixed-rate liability.
We have outlined the basic principles of theIRBBB. We can now move on and analyse inmore detail the new standards: in doing that,we will have the opportunity to extend the anal-ysis so as to include credit and funding spreads.
The Economic Value and the Net Interest In-come in the New Standards
In the Basel Committee’s view, the EV and theNII metrics are complementary (see par. 34, [3]),in terms of:
• Outcomes: EV measures compute thechange in the net present value of thebank’s assets, liabilities and off-balancesheet items subject to specific interest rateshock and stress scenarios, while NII mea-sures focus on changes to future profitabil-ity within a given time horizon. This istrue since the NII is calculated on an un-discounted basis and the yearly P&L ofthe Bank attributable to the net interestincome is calculated on a yearly cash-flowbasis, as we have seen above;
• Assessment horizons: EV measures reflectchanges in value over the remaining life ofall the contract in the bank’s assets, liabili-ties and off-balance sheet items, while NIImeasures cover only the short to mediumterm horizon, and therefore do not iden-tify the risks the may appear until the ex-piry of all the (interest rate-sensitive) con-tracts in the Bank’s balance sheet. Alsoin this case, the statement is true sincethe two metrics are not computed over anidentical horizon. In reality, we saw that
the two metrics could identify the samerisks if they are computed so that compa-rability is possible;
• Future business/production: EV measuresconsider the net present value of cashflows only of instruments on the bank’sbalance sheet or accounted for as an off-balance sheet item at the reference date(run-off perspective); NII measures may,in addition to a run-off view, assumerollover of maturing items (constant balancesheet perspective) and/or future business(dynamic perspective).
The consideration above is somehow limited byPrinciple 8, where for comparability purposesit is mandated that the EV and NII metrics becomputed following a specific set of rules. Welist (in italic) the rules and comment on each ofthem in some detail.
Banks should compute the variations of theEV, i.e.: DEV, under the prescribed interest rateshock scenarios, complying with the followingrules:
• Equity should be excluded from the computa-tion of the exposure level.
Some banks model also the equity for IR-RBB purposes, but we think that, in theend, the EV is just the value of the eq-uity, or the difference between the (ex-pected) present value of the assets, liabil-ities and off-balance sheet items.12 Alter-natively, the stream of net interest incomethat flows to the equity is just the result ofthe algebraic sum of the interests receivedand paid. So, in either cases, it would be
12We already mentioned above that considering the equity as a simple difference of the present value of the assets andliabilities is not correct, since we are missing the interdependency between all of them, which makes the balance sheet anindivisible bundle of contracts whose value is the true value of the equity.
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rather meaningless including in the com-putation of the EV, or of the NII, also thecash-flows related to the equity. Moreover,including the equity would reduce the riskexposures, by considering modellable a li-ability whose maturity is undefined andwhose intermediate payments depend onthe P&L of the assets and other liabilities.
Hence, the modelling would be basicallyarbitrary and concealing risks that wouldnot be recognised, since trivially and tau-tologically they are hedged out by the as-sets that theoretically replicate the cashflows or the risk profiles related to theequity. The hedge would perfectly workby definition, but the equity would rarelyproduce the same economic results as thereplicating portfolio of assets, if only forthat its variations on a given time horizon(say, one year) contribute to the variationof the equity itself via the P&L they gen-erate.
A very simple example will illustrate whythe modelling of the equity is rather sus-picious. Assume that the Bank just startedat the reference time t0 and that in itsbalance-sheet there are only cash on theasset side, and the equity on the liabilityside. The equity is modelled as 10 yearmaturity liability paying a fixed rate; tomatch this exposure, the Bank invests thecash in a 10 year maturing bond, payinga fixed rate too. In Figure 6 we show thecash-flows up to 10 years.
If we compute the EV including the equity,we have trivially that it is zero; moreover,if we recompute it in a given scenario, saythe interest rate term structure up 200 bps,it is manifest that the DEV is similarly nil.Nonetheless, it is quite clear that, if theEV has to show the net sensitivity of thesum of the market values of the assetsand the liabilities, when including the eq-uity the metric will provide a completelymisleading value. In our simple example,DEV = 0, when in reality the shareholdersbear the market risk of a 10-year fixed-rateinvestment, which is obviously substantial.So, when modelling the equity, the Bankis dangerously reducing the exposure tointerest rate movements for an amountequal to the equity itself.
Considering now the NII, it is also quitemanifest that it is trivially zero, and so
is its sensitivity to any interest rate sce-nario. Therefore, in this case too, the met-ric would show no risk at all borne by theshareholders. Admittedly, if the NII is justthe net income due to interest rates, sincethe investment matures in 10 years andthere is no repricing risk, in our examplethe DNII would be zero even without theinclusion of the equity.
For the NII, a misleading indicationwould arise should the Bank model theequity as a 10-year floating-rate liability(contrarily to the a fixed rate asset as be-fore): in this case, the inclusion of theequity would again produce a zero NIIsensitivity, whereas in reality the share-holders are fully exposed to interest ratesmovements for the payments related tothe coupons.
In conclusion, we believe that the equityshould not be included in the calculationof both NII and EV. In case the Bankhas free funds to invest, the decision toallocate them should be based on the riskappetite set for the sensitivity of the NIIand EV, and on the profitability targets.As such, this is just an investment deci-sion that does not require any (suspicious)equity modelling.
• All cash flows from all interest rate-sensitiveassets, liabilities and off-balance sheet itemsin the banking book should be included in thecomputation of the exposure. Banks should dis-close whether they have excluded or includedcommercial margins and other spread compo-nents in their cash flows.
This rule is quite puzzling: if all cash-flows should be included, why should theBank disclose if commercial margins orother spreads are excluded? The first partof the prescription seems to forbid theexclusion, but the second part implicitlyallows that. In any case, if the marginand/or other spread components are ex-cluded, the present value of all the balancesheet’s items will be strongly affected. Wecannot see why these components shouldbe excluded from the calculation of theEV. On the other hand, it is true thatthe expected NPV of any contract shouldrecognise all the risks that it bears.
For example, in a corporate loan, thecredit spread over a reference risk-free rate(say, the Eonia) has to be included in the
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cash-flows, but also the probability of thecounterparty’s default, and consequentlythe possibility that the cash-flow does notoccur, should be take into account as well.On an expectation basis, the total defaultrisky cash-flow would equal the risk-freecash-flow, if the credit spread is fair.
To make things concrete, let us go back toour stylised balance sheet in section 3.1.1,and let us assume that the asset is nowsubject to default risk: there is a constantyearly probability of default of 1%. In caseof default, the Bank receives 40% of thenotional of 1,000,000.00, so that the lossgiven default is Lgd = 60%. The NPVof the asset should be computed by thefollowing formula:
A1 =IE
Âi=0
D(t0, ti)cf(t0, ti; A1) =
=IE
Âi=0
D(t0, ti)⇥ c ⇥ N ⇥ [1 � PD(t0, ti)]+
+D(t0, ti)⇥ N ⇥ [1 � Lgd]⇥
⇥ [PD(t0, ti)� PD(t0, ti�1)]
�
(13)
where PD(t0, ti) is the probability thatthe asset defaults between t0 and ti, Nis the notional of the asset and c is thecoupon. In the default-free risk case, theasset had a coupon c = 2.50%, which wasfair given the interest rate curve at timet0, so that the NPV was just the notional1,000,000.00. When accounting for the de-fault risk, given the parameters of PD andLgd provided before, we derive the faircoupon by recursively solving equation(14), setting A1 = 1, 000, 000.00 (the cashpaid to the debtor in t0): the result isc = 3.1052%.
The credit spread is s = 3.1052% �2.50% = 0.6052%. The new cash-flowschedule, considering also the possibilityof a default occurrence, is
Asset LiabilityInterest Capital Interest Capital
34,741.74 17,748.3734,394.32 17,748.3734,050.38 17,748.3733,709.87 17,748.3733,372.77 17,748.37 1,000,000.0033,039.0432,708.6532,381.5732,057.7531,737.17 904,382.08
Each cash-flow referring to the asset hasbeen weighted for the probability of itsoccurrence, has indicated in equation (14).
The EV is the sum of the discounted cash-flows of two contracts, so that we haveagain that:
Assets LiabilitiesA1 = 1, 000, 000.00 L1 = 1, 000, 000.00
——————–E = 0.00
Let us check what happens to the sensitiv-ity to a given scenario of the EV. Considerthe “200bps UP” scenario we have definedin section 3.1.1, and calculate the EVPU ,which now equals to 843, 814.52, so thatDPUEV = �64, 260.72. This is a quite dif-ferent figure than DPUEV = �70, 834.59obtained without considering the creditspread and the probability of default.
In conclusion, we believe that the creditspreads and all other margins, includingthe funding spreads, should be includedin the calculation of the EV, by consider-ing also the additional adjustments thatare due to the risks they are meant to re-munerate. In the example we presented,the cash-flows are adjusted by weightingthem with the probability of their occur-rence implicit in the default probability ofthe asset. So the first part of the provisionwe are discussing should be consideredas sensible and correct under a theoreticalpoint of view. We suggest to just disregardthe second part of the rule, if only to avoidconsidering the Regulator subject to someform of self-denying attitude.
It is worth stressing that, while the creditspread is set at the origination of the con-tract, based on the conditions deemed fairby the market (or by the Bank) at that time,during the life of the contract the PD andLgd may change so that the weighting ofthe cash-flows may be different from those
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used at the inception (the current levels ofthe two variables are extracted from thestarting credit spread curve T C appliedto the obligor or issuer of the security).This may cause additional effects on thesensitivity of the EV that should not beexcluded.One last remark is about the default riskof the Bank itself in computing the EV: inour opinion it should not be considered,both for prudential reasons in calculatingthe risk metrics, and to comply with a go-ing concern principle, according to whichthe Bank is assumed to run its activitieswithout a specific terminal date. The varia-tions of the Bank’s PD and Lgd should betaken into account, instead, since they canaffect the funding spread paid on rolledover liabilities.This rule seems to be against the implicitassumption the that EV is the sum of theliquidation values of the contracts in thebalance sheet. Actually, by disregardingthe possibility of its own default, the Bankis not computing the EV according to theimplicit assumption; nonetheless, we be-lieve that the metric calculated in such away is more representative of the value tothe shareholders (which is what ultimatelymatters), and besides it provides a moreaccurate sensitivity to a given scenario.13
We extend the example shown above, byassuming the Bank can default and there-fore it pays a credit spreads on its lia-bilities: the credit spread is considereda funding spread from the Bank’s pointof view. Let the spread paid over the risk-free coupon 1.77% be equal to 0.5%. Thecash-flows modify as follows:
Asset LiabilityInterest Capital Interest Capital
34,741.74 22,748.3734,394.32 22,748.3734,050.38 22,748.3733,709.87 22,748.3733,372.77 22,748.37 1,000,000.0033,039.0432,708.6532,381.5732,057.7531,737.17 904,382.08
The cash-flows on the liability sideare simply given by (1.77% + 0.5%) ⇥
1, 000, 000.00, without any weighting forthe occurrence probability, contrarily towhat we did for the asset side. The result-ing NPV of the asset and liability, usingthe risk-free discount factors in Table 2, is:
Assets LiabilitiesA1 = 1, 000, 000.00 L1 = 1, 023, 953.31
——————–E = �23, 953.31
and the EV = �23, 953.31. Had we usedthe weighting of the cash-flows by theBank’s PD, and the recovery rates on de-faulted cash-flows, we would have gotan NPV of 1,000,000.00 of the liability aswell. Disregarding the Bank’s default (butnot the funding spread) leads to a higherNPV and hence a lower EV, which is nownegative. In any case, since we are actu-ally interested in the risk related to thechange of the EV, we recompute it in the“200bps UP” scenario, and we get EVPU =�86, 846.72, so that DPUEV = �62, 893.41,which is not very far from the case abovewhen only the asset was subject to defaultrisk.
• Cash flows should be discounted using either arisk-free rate (an example of an acceptable yieldcurve is a secured interest rate swap curve) ora risk-free rate including commercial marginsand other spread components (only if the bankhas included commercial margins and otherspread components in its cash flows). Banksshould disclose whether they have discountedtheir cash flows using a risk-free rate or a risk-free rate including commercial margins andother spread components.In our opinion, there is only one admis-sible curve to discount future cash-flows,and it is the risk-free curve.14 The risk-freecurve should be based on the Eonia swaprates quoted in the market: these rates re-fer to the Eonia rate, i.e.: an overnight in-terbank loan rate, which for its very shortduration embeds the smallest (negligible)amount of credit spread component. So,even if we consider a 10 year expiring Eo-nia swap, as far as the contract is con-tinuously collateralised (as it is the casefor contracts in the interbank market), thecredit spread is in any case the tiny onerelated to a 1 day expiry loan.
13The correct way to compute the value to the shareholders is outlined in Castagna [6]: based on the results therein, theexclusion of the Bank’s default does not guarantee a correct computation, but the results are nearer to the theoretically exactvalue to the shareholder.
14See Castagna [5] for a discussion on this point.
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Discounting cash-flows by an effectiverate, i.e.: a rate that includes a risk-freeand a credit spread component, is a short-cut to account for the credit risk and possi-bly additional costs (e.g.: funding spreads).Anyway, we think that this approach is notclear under a theoretical point of view andit takes a greater effort to be dealt with un-der a practical point of view. The best wayto properly evaluate the NPV of a con-tract is to consider all the expected cash-flows (including shortfalls due to creditrisk and other behavioural options, andother costs).To make things concrete, working withan effective rate that includes a creditspread (and/or other margins), meansthat the NPV of a contract is not computeby means of equation (14), but with thefollowing:
A1 =IE
Âi=0
De(t0, ti)cf(t0, ti; A1) =
=IE
Âi=0
De(t0, ti)⇥ c ⇥ N+
+De(t0, ti)⇥ N
(14)
where De is an effective discount factorthat includes the credit spread. For ex-ample, assume as before that PD = 1%and Lgd = 60%: the annual expected lossis EL = 1% ⇥ 60% = 0.60%. To adjustthe discount factor so that it considersthe credit spread, one should multiply theoriginal, risk-free discount factor D(t0, ti)by the amount
exp[� ln(1 + EL)⇥ (ti � t0)] =
exp[� ln(1 + 0.6%)⇥ (ti � t0)]
So, De(t0, ti) = D(t0, ti) ⇥ exp[� ln(1 +EL) ⇥ (ti � t0)]. This is the most soundway to include into the discount factor thecredit spread, under the assumption thatthe Lgd is the a percentage of the marketvalue of the asset, rather than the notionalamount, at the default event.If the Bank uses the effective discount fac-tors in computing the EV and DEV, theresult does not significantly differ fromthe case that we have analysed before,
and that we consider the most appropri-ate. When using this approach for theliabilities, one cannot exclude the defaultprobability of the Bank in evaluating theNPV of the liabilities. We mentioned be-fore that we would prefer not to includethe default in the calculation of this case,even though the funding spread shoulddefinitely enter in the cash-flows paid.15
• DEV should be computed with the assump-tion of a run-off balance sheet, where existingbanking book positions amortise and are notreplaced by any new business.
The rule is sensible if the measure is aim-ing at determining the current net (liquida-tion) value of the Bank’s balance-sheet,16
but it poses some concerns when consider-ing all the funding costs that are going tobe missed, since the roll-over of the exist-ing liabilities is not considered. In reality,if a funding spread over the risk-free rateis paid by the bank, the (if only expected)future cost related to the funding of assetsshould not be disregarded.
More specifically, the Bank will typicallyoperate a maturity transformation to buyits assets, so that the average maturity ofthese will be longer than the average ma-turity of the liabilities. When computingthe EV as the sum of the NPVs of both as-sets and liabilities, one does not considerthe fact that liabilities have to be neces-sarily rolled over to preserve the financialbalance constraint, at least until the ex-piry of the longest maturing asset. Now,if the Bank is able to raise funds at therisk-free rate, i.e.: at the same rate used todiscount cash-flows, the NPV of the liabil-ities would be the same in any case, eitherconsidering or disregarding the roll-over.This result has been shown in the stylisedbalance sheet of section 3.1.1: the EV hasthe same sensitivity of the discounted NIIup the maturity of the longest contact (10years in the example), and the only differ-ence between the two metrics is the roll-over in the latter, which is missing in theformer. As per Fact 2, as far as the risk sen-sitivity is concerned, the EV can be seenequivalent to a discounted NII up to thematurity of the longest contract, and, con-
15For a more in depth discussion of these aspects, we refer once again to Castagna [5].16It should be noted that the liquidation at market values is performed on a single contract basis, or at least on the basis
of groups of contracts referring to the Bank’s counterparties. The value of the Bank, seen as a bundle of contracts, has adifferent value from the algebraic sum of the NPVs of the single assets and liabilities. See Castagna [6].
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versely, the NII equivalent to an EV with-out a roll-over of the expiring liabilities,provided no credit risk, and consequentlyspreads, exist.
When the Bank must pay a funding spreadto remunerate the credit risk born by itscreditors, then disregarding the roll-overof the liability will underestimate their(negative) NPV, and thus will overesti-mate the EV, and will in the end providean inaccurate sensitivity to a given sce-nario. To see this effect in practice, wetake back the example in the point abovewith credit risk on the asset and fundingspread, and we calculate the EV under theassumption of a constant balance sheet,this making it indistinguishable from adiscounted NII. The (expected) cash-flowsare:
Asset LiabilityInterest Capital Interest Capital
34,741.74 22,748.3734,394.32 22,748.3734,050.38 22,748.3733,709.87 22,748.3733,372.77 22,748.37 ± 1,000,000.0033,039.04 38,360.6232,708.65 38,360.6232,381.57 38,360.6232,057.75 38,360.6231,737.17 904,382.08 38,360.62 1,000,000.00
After 5 years, the expiring debt is rolledover, and the new coupon is given bythe forward 5-year coupon implied in thecurve, which we know to be 3.3361%, plusa constant funding spread of 0.5%, as be-fore. The EV = �44, 763.12, as shownbelow:
Assets LiabilitiesA1 = 1, 000, 000.00 L1 = 1, 044, 763.12
——————–E = �44, 763.12
When computing the sensitivity to theusual “200bps UP” scenario, we get anEVUP = �104, 610.71:
Assets LiabilitiesA1 = 843, 814.52 L1 = 948, 425.23
——————–E = �104, 610.71
so that DPUEV = �59, 847.59, comparedto DPUEV = �62, 893.41 when roll-overwas considered.It could be argued that the difference be-tween the two figures of DPUEV is notreally material: this can be partially ac-cepted as an argument, but the real pointmissing in the DPUEV considering the roll-over is the possible change in the fundingspread paid by the bank when reissuingthe new bond to replace the expiring one.None of the scenarios provided by theBasel document [3] refer to a change inthe funding spreads, so apparently theBank would be fully compliant with theRegulator’s requirements. Nonetheless,since the same document mentions (with-out elaborating too much, admittedly) theCredit Spread Risk of the Banking Book(CSRBB) as a risk to be monitored and as-sessed, we think that the impact on the EVof funding spread changes should be in-cluded, together with the changes causedby credit spreads on the assets.17
When monitoring and assessing theCSRBB, we believe that disregarding theroll-over would strongly underestimatethe risk borne by the Bank.In any case, to conclude this comment, abetter rule would have prescribed a roll-over of the liabilities for the necessaryquantity and duration to allow for thefunding of the longest maturing asset: inthis way, if a funding spread is projectedfor the future renewal of the maturing li-abilities, a more correct and prudent EVwould have been calculated.
Banks should also compute the variationsof the NII, i.e.: DNII, under the prescribed in-terest rate shock scenarios, complying with thefollowing rules:
• Banks should include expected cash flows (in-cluding commercial margins and other spreadcomponents) arising from all interest rate-sensitive assets, liabilities and off-balance sheetitems in the banking book.The rule is clearer and more definitivethan the equivalent rule set for the EVmeasure: all the margins and spread com-ponents do belong to the set of cash-flows
17For EV calculation purposes, the change in the PD’s and Lgd’s of the issuers of the assets held by the Bank does notany material impact on the spread paid over the market rate (e.g.: the 6M Euribor) but in the rare cases these assets bear acoupon paying an adjusting floating spread over the risk free rate. The change has a material effect in calculating the NPV ofthe assets (or in the evaluation of the NPV of derivatives hedging the credit risk) as in can be easily seen, for example, fromequation (14), when considering the coupon c contractually fixed.
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received on assets and as such they shouldbe included the in NII calculation: nodoubt arises from a self-denying wording,as in the ev case.
At the same time, it is also reasonable toinclude only the expected values of thecash-flows, as we have discussed before.The expected value is a function of mar-ket variables, as for example in the casewhen an interest payment is linked to anindex (e.g.: a floating interest rate linkedto the 3M Euribor); the expected value isalso dependent on credit events (e.g.: itshould consider the total or partial loss oc-curring when the debtor defaults), or onbehavioural optionalities (e.g.: the prepay-ment of a mortgage will alter the paymentschedule).
• DNII should be computed assuming a con-stant balance sheet, where maturing or repric-ing cash flows are replaced by new cash flowswith identical features with regard to theamount, repricing period and spread compo-nents.
The rule is the opposite of the rule set forthe EV, since it basically provides for theroll-over of the maturing positions. Thefact that the roll-over is operated by replac-ing the maturing contract with a new onewith the same features, may cause someproblems. For example, it is sensible toassume that the risk-free component ofthe contract should be determined on thebase of the forward rates implied in thecurves at the reference (i.e.: calculation)time; the same rule can be applied forthe funding spread paid by the Bank onthe new liabilities replacing the maturingones: these spreads could be computedout of the funding spread curve prevail-ing at the reference time. But this meansalso that the commercial margin for therolled-over assets should consider the newfunding spread paid by the Bank.18 Thesame considerations can be made for thecredit spread margin on the rolled assets:if a credit spread term structure is avail-able, the Bank could apply the spreadsimplied within it to determine the newmargin to apply.
In the end, if the Bank adopts the ap-proach to compute the expected future val-
ues of the cash-flows based on the interestrate curves and funding and credit spreadcurves prevailing at the reference date,it will not strictly comply with the ruleprovision to roll-over the contracts withthe same identical features. But we thinkthat the rule can be interpreted so that thecontracts should be identical as far as theexpiry, the amortisation mechanism andthe type of interest rate (fixed/floatingand frequency) are concerned; at the sametime, they can be renewed consideringalso the expected values of the relevantquantities to determine the cash-flows.
• DNII should be disclosed as the difference infuture interest income over a rolling 12-monthperiod. We have investigated the relation-ships between the EV and the NII above:we know that basically, when accountingfor discounting, the two metrics providethe same information. In practice, the cal-culation of the NII may be operated untilthe expiry of the longest contract in thebalance sheet, or even further, but for reg-ulatory purposes the DNII has to be re-ported only for a period of one year fromthe reference (calculation) date, and with-out any discounting.This could be deemed too short a periodthat does not allow to identify risky as-sets’ and liabilities’ configurations: wehave already discussed the possible mis-leading indication provided by the NIIwhen the bank operates in a regime ofmaturity transformation, and the capitaldepletion due to the annual distributionof dividends when the cash-flow patternis not evenly split until the expiry of theassets and the liabilities.Anyway, when the DNII is observedjointly with the results of the DEV, someof these deficiencies are overcome, sincethis joint monitoring will reveal trouble-some situations due to the shorter dura-tion of the liabilities. For example, a posi-tive NII for the next year, with a slightly(or even nil) negative sensitivity to an up-ward shift of the interest rate term struc-ture, could be observed jointly to a highnegative sensitivity to the same upwardshift, of the EV, indicating that the bankis aggressively relying on maturity trans-formation, funding short-term assets with
18The commercial margin refers to assets where the Bank has some, or full, pricing power, such as loans and mortgages.Obviously, it does not apply to traded securities for which the Bank can only accept the yield set by the market.
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longer maturity. The low earning volatil-ity is counterbalanced by a the higher eco-nomic value uncertainty.
The Standardised Framework
In addition to the twelve principles to be usedas guidelines for the setup of an internal model,the BIS has set out a standardized model whichallows for the assessment of IRRBB based solelyon a DEV calculation on six predetermined in-terest rate shock scenarios. Such model is in-tended for banks which (according to the rela-tive Supervisors) do not meet the necessary re-quirements to rely on an internal risk structure;however, on a broader basis, it can be adoptedby any bank that wishes to comply to the newregulation without following an internal modelapproach.
Since the BIS document [3], for standardisedapproach, dwells on the contracts subject to be-haviuoral optionalities (positions not amenable tostandardisation), in commenting the guidelineswe have the chance to hint at some more ad-vanced modelling approaches to take accountmore satisfactorily the risks embedded in thosebalance sheet items.
Standardised Interest Rate Shock Scenarios
The key components of the standardizedmodel for IRRBB are the six scenarios prescribedby the BIS, under which the sensitivity of Eco-nomic Value of Equity to interest rates is calcu-lated. The six scenarios are composed, for theinterest rates term structures each currency c, asfollows:19
• Parallel shocks (down and up):
DRparallel,c(tk) =Jparallel,c(tk) =
=± Rparallel,c(tk)(15)
• Short rate shocks (down and up):
DRshort,c(tk) =Jshort,c(tk) =
=± Rshort,c(tk)e(�tk/4) (16)
where the exponential scalar is expresslyset up to have a greater impact on theshorter tenors tk of the term structure,while fading to 0 on the longer tenors.
• Rotation shocks (steepener and flattener):
DRsteepener,c(tk) =Jsteepener,c(tk) =
=� 0.65|DRshort,c(tk)|++0.9|DRlong,c(tk)|
(17)
DR f lattener,c(tk) =J f lattener,c(tk) =
=0.8|DRshort,c(tk)|+�0.6|DRlong,c(tk)|
(18)
where
DRshort,c(tk) =Jshort,c(tk) =
=± Rlong,c(tk)[1 � e(�tk/4)]
The currency specific shocks Rshocktype,c neededto compute the scenario bumps described aboveare contained (in basis points) in the table in Fig-ure 3, which is taken from the BIS document [3].We tried also to keep as much as possible theoriginal notation of the BIS document [3] andreconcile it with the one we introduced above.
The shocks are recalibrated every five yearsby the Basel Commitee to align them to the localmarket conditions. The calibration procedure isexplained in the Annex 2 of the BIS document[3] and can be easily replicated by the Bank.
19We try to use the same notation as in the BIS document [3] for the definition of the scenarios, connecting it with the oneintroduced above in this work.
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Parallel Short LongARS 400 500 300AUD 300 450 200BRL 400 500 300CAD 200 300 150CHF 100 150 100CNY 250 300 150EUR 200 250 100GBP 250 300 150HKD 200 250 100IDR 400 500 350INR 400 500 300JPY 100 100 100
KRW 300 400 200MXN 400 500 300RUB 400 500 300SAR 200 300 150SEK 200 300 150SGD 150 200 100TRY 400 500 300USD 200 300 150ZAR 400 500 300
TABLE 3: Standard shocks (in bps) to apply to the reference risk interest rate curve, per currency.
Perimeter and Categorisation
All items (including off-balance sheet ones) inthe banking book are subject to the process ofIRRBB exposure calculation except for: liabil-ities included in CET1 capital computation asper the Basel III framework, assets which arededucted from CET1 capital, fixed assets, intan-gible assets and equity exposures. The secondrestriction on the application perimeter of thismodel, is that only products denominated incurrencies on which the bank has material ex-posure are considered for the calculations. Theterm “material exposure” refers to currenciesthat make up for at least 5% of total asset orliabilities in the banking book.
From each of the included items, the bankstrips out a series of notional repricing cashflows which can be considered the buildingblocks of the calculation process. Notionalrepricing cash flows include the following types:
• Notional repayments at contractual matu-rity;
• Notional repricings, which occur on theearliest date at which the bank or thecounterparty can autonomously modifythe underlying rate, or when a floatingrate changes following a change in thereference index;
• Notional tranche payments and interestpayments that have yet to be repaid orrepriced.
The bank has also to declare in a transparentway whether it decides to include, or exclude,the fractions of notional repricing cash flowslinked to spreads: these include any commer-cial, credit and funding margins added to thecontractual indexations. The general consider-ations we have presented above about the ex-clusion of margin components from cash-flowsapply also to in this case.
Once the perimeter of the banking bookitems has been clearly identified, the notionalrepricing cash flows are subdivided into threemain categories. Each of these includes dealsfor which it is increasingly difficult to determinethe timing of contractual rate shocks and theirimpact on the bank’s balance sheet:
• Positions amenable to standardization: in-clude fixed and floating rate items with noembedded behavioral optionalities. If anautomatic optionality (such as a cap/flooror callability) is included, this is strippedout of the contract: the “simple” cashflows are slotted in this category, whilethe optional components are allocated tothe next category.
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Time bucket intervals (M: months; Y: Years)
Short-termrates
Overnight(0.0028Y)
O/N <tCF1M(0.0417Y)
1M <tCF3M(0.1667Y)
3M <tCF6M(0.375Y)
6M <tCF9M(0.625Y)
9M <tCF1Y(0.875Y)
1Y <tCF1.5Y(1.25Y)
1.5Y <tCF2Y(1.75Y)
Medium-termrates
2Y <tCF3Y(2.5Y)
3Y <tCF4Y(3.5Y)
4Y <tCF5Y(4.5Y)
5Y <tCF6Y(5.5Y)
6Y <tCF7Y(6.5Y)
Long-termrates
7Y <tCF8Y(7.5Y)
8Y <tCF9Y(8.5Y)
9Y <tCF10Y(9.5Y)
10Y <tCF15Y(12.5Y)
15 <tCF20Y(17.5Y)
tCF >20Y(25Y)
TABLE 4: Time bucket grid for cash flow slotting.
• Positions less amenable to standardization:include all the explicit or embedded au-tomatic interest rate optionalities whichhave been separated from the original con-tracts.
• Positions not amenable to standardization: in-clude all deals with embedded behavioraloptionalities, namely: Non-Maturing De-posits (NMDs), fixed rate loans with pre-payment risk and deposits with early re-demption risk.
Positions amenable to standardization
Each notional repricing cash flow extracted fromdeals allocated to this category is firstly asso-ciated to one of the time buckets contained inFigure 4, taken from the BIS document [3]. Theterms in brackets are the midpoints of eachtime bucket, which are indicated with tk, withk 2 {1, ..., 19}.
The proviso in point 104 (pg. 24) of the BISdocument [3] assumes that all floating rate in-struments are slotted in the first bucket withinwhich the next repricing date occurs, with-out any further slotting except for the possi-ble spread components that do not reprice onthat date. We understand that within a stan-dardised approach aiming at simplifying thecalculations, such a rule may be accepted, eventhough we cannot help but feel disconcertedby the approximations it produces, which canbe also substantial in some financial conditions.The main simplifying assumption here is thatthe interest rate index, to which the instrumentis linked, is the same used to build the discount-ing curve, so that the NPV is just equal to lastfixed coupon plus the notional, discounted from
the next payment (equal to the repricing) date.It is quite manifest that currently discount-
ing curves are dependent on the reference indexused to build them, so that the curve based onEonia swap prices, which we argued is the cor-rect discounting curve, is quite different fromthe discounting curve bootsrapped from fixed-to-6m-floating swap curves. Thus the simpli-fying assumption may produce relevant distor-tions in the calculation of the DEV, withoutmaking life so much easier to the people in-volved in the process, we believe. If the Bankcan override the rule and correctly price thefloating rate instrument, we would suggest todo so.
Positions not amenable to standardisation
i) Non Maturing DepositsNon maturing deposits (NMDs) are depositswhich do not have a specified maturity: thistype of contract will therefore be subject to re-demption risk. There are two steps to follow:
1. Segmentation of non maturing depositsin i) retail and ii) wholesale deposits. Theretail deposits include those owned byindividuals and small businesses (whichare identified as business toward whichthe bank has less than 1 million in totalnotional exposure); they are further di-vided between a) transactional and b) non-transactional deposits, depending on thefrequency of transactions being carried onand from the deposit account.20 This cat-egorisation will affect the slotting, as wewill explain in a moment.
20Deposits bearing no interest are assumed to be transactional.
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Cap on proportion of core deposits Cap on average maturity of core deposits(years)
Retail/transactional 90 5Retail/non-transactional 70 4.5
Wholesale 50 4
2. Separation in two parts: i) stable and theii) non-stable, of each NMD category iden-tified in step 1, using observed volumechanges over a the past 10 years. The sta-ble part is defined as the portion of NMDsthat is not withdrawn with a high degreeof likelihood. The BIS document [3] doesnot specify how to determine this likeli-hood. One possibility is compute the dis-tribution of the variations of the depositsvolumes over the previous 10 years andthen choose a predefined percentile (saythe 99th of the negative variations) anddeduct it from the volumes in the balancesheet at the reference time. The stable partis further split in i) core deposits, i.e.: theproportion of stable NMDs which are notlikely to reprice to changes in the mar-ket interest rates; and ii) non-core deposits,which conversely are most likely repricedwhen market interest rate changes.
The proportion of core deposits, inside eachcategory, is subject to slotting within the reg-ulatory buckets. The quantity of deposit toassign to each bucket is left to the Bank, pro-vided it complies with the regulatory caps forthe core proportion and the average maturity,as described in the table below (taken from theBIS document [3]. Non-core deposits are to beslotted into the overnight bucket by default.
It is worth noting that the final BIS docu-ment [3] outline the treatment of NMD in verygeneral terms, in any case in much less detailthan the consultative document [2], thus leav-ing the Bank with some degree of freedom inadopting specific modelling choices that can bequite crucial, especially in the current low, oreven negative, interest rate environment. Forexample, the footnote 32, at page 20, of the con-sultative document [2], explicitly asserted theequivalence between the non-core proportion ofstable deposits and the fraction of the (variationsof) market interest rate passed through to de-posits. This equivalence is based on the verycommon approach adopted in the banking in-dustry to deal with NMD, which unfortunately
in the current financial environment show somedeficiencies.
In more details, the common banking indus-try approach relies on two assumptions:
1. NMDs bears an interest rate which is al-ways a fraction of the market interest rate(say: the 1M Euribor), or, alternativelysaid, NMDs are a liability yielding a posi-tive carry;21
2. market interest rate cannot be negative.
Now, the first assumption can be true most oftimes, but surely it showed to be false in someperiods, for reasons related to general marketrisk (including country risk) and idiosyncratic,bank specific risk. We observed, in the recentpast, that deposits’ rates were well above shortterm interest rates to avoid bank runs or to usedeposits as a source of funding for the ordi-nary bank activity, hence competing with otherlonger term sources. The second assumptionis false since the ECB started setting the ratesat negative levels, pushing in negative territoryalso short term market rates. When one or bothassumptions do not hold, the equivalence of thenon-core proportion of stable deposits and thefraction of the market rate passed through fails.
To see this, let us see formally where theequivalence comes from: very generally, the to-tal variation of the interest paid by the Bank onthe deposits at a given time t is:
DI(t) = Di(t)⇥ D(t)
where i(t) is the deposit rate and I(t) is thetotal interest paid on the amount of depositsD(t). Assume that the Bank makes an estima-tion of the pass-though fraction of market rater(t) to the deposits, by means of a statisticallinear regression on the past data of the kind:
Di(t) = bDr(t) + #(t)
By the properties of the OLS, the expectedvalue of Di(t) is:
E[Di(t)] = bDr(t)21It is implicitly assumed that the carry is positive since deposits are reinvested at the prevailing short term (e.g.: 1M
Euribor) without considering the cost of the buffer held to hedge the liquidity risk, or: the possible zero yield on the volatilepart of the deposit, which should be in theory held in cash.
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The coefficient b represents the pass-thoughrate, and also the fraction of deposits thatreprice accordingly to market rates’ movements,as it can be easily shown by rewriting the equa-tion above so that we have a direct dependenceon the market rate’s change, although on a frac-tion b of the entire deposit volume D(t).
DI(t) = bDr(t)⇥ D(t) = Dr(t)⇥ bD(t)
As such, b must be a value between 0 and 1 (i.e.:0 b 1): this is a constraint that must beset when estimating the linear regression above,even though the coefficient can well be greaterthan 1 in reality.
Moreover, by simple manipulations and re-cursion, we have:
E[i(t)] = a + br(t)
where a = i(0) � br(0). The last equationshows that the first assumption is a result ofthe constraint on b, if a is enough small or zero.Nevertheless, when the short term market rateis negative, the deposit rate has to be alwaysgreater and negative as well, or r(t) i(t) 0.This means that the Bank is paying more thanthe market rate on the deposits, and the carryswitches from positive to negative. This canreflect the actual pricing behaviour of the Bank,but it cannot capture a pricing policy which pre-serves the smaller deposit rate with respect toshort term market rate (or: a positive carry fromthe deposits’ liability).
Another drawback due to the equivalence ofthe pass-through rate and the proportion of non-core deposits is that when there is a floor at zeroon the rates paid on deposits, this pricing policycannot be captured at all.22 Actually, the rela-tionship cannot be linear, when a floor optionsis (even implicitly) granted to depositors.
As far as the cash-flow slotting is concerned,we find rather surprising the allocation of theentire non-core partition of deposits in the O/Nbucket: this choice implies that the bank isactually repricing the NMDs on a daily ba-sis, which is quite unusual in our experience.To cope with the assumption implied in theBIS prescription, the Bank should estimate thepass-through linear relationship above betweenthe deposit rate and the O/N market rate, sothat the pass-through rate/non-core proportion
equivalence provides a meaningful slotting onthe first bucket. Anyway, it should be stressedthat the final BIS document [3] leaves the Bankfree to estimate in the way it deems the mostappropriate.
Finally, it should be stressed that the stan-dardised approach does not link the evolutionof the deposits’ volume to the market interestrates’ changes: it is documented that a negativerelationship exists between the two quantities,which cannot obviously be considered withinthe BIS framework. It is easy to check that in thecalculation of the EV according to the standard-ised approach, the slotting of the initial deposits’volume is unaffected by any of the predefinedsix scenarios, hence confirming the substantialdichotomy between the evolution of the marketinterest rates and the deposits’ amount.
We have presented the main flaws of thestandardised approach to highlight the fact that,even if it is supported by the BIS document [3]as an acceptable alternative to proprietary mod-els, it should be replaced by a more advancedframework if the Bank wishes to better measureand manage its risks. In Castagna e Fede [8], ch.9, we present one of such advanced approaches,which we name stochastic risk factor; for a furtherdevelopment of this approach and an applica-tion to real market and balance sheet data, werefer to Castagna and Scaravaggi [9], where awide range of metrics and risk measures areintroduced and computed in practice, even ifbeyond the mere interest rate risk monitoring.
Other instruments with embedded behav-ioral options that do not classify as NMDs aretreated separately. They range on all deals forwhich the customer’s choice (based on the ob-served movements of market interest rates) isable to modify the magnitude and the timingof the cash flows expected by the bank. Op-tions owned by wholesale customers, whichare treated as automatic options in the “lessamenable to standardization” category, are ex-cluded from the following procedures.
ii) Fixed-Rate Loans Subject to Prepayment RiskBanks bear a major behavioural risk, affectingboth liquidity and financial risks too, on loanproducts. Sometimes, due to existing laws ormarketing choices, a prepayment fee is not evenexplicitly defined in the contract.
22Floors at zero are usually set for retail deposits. In some countries, they are prescribed by the law for non corporatedeposits.
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Banking Book
Scenario number (i) Interest rate shock scenarios yi (scenario multiplier)1 Parallel up 0.82 Parallel down 1.23 Steepener 0.84 Flattener 1.25 Short rate up 0.86 Short rate down 1.2
TABLE 5: Parameters g for the standardised scenarios to calculate the conditional constant prepayment rate.
Scenario number (i) Interest rate shock scenarios yi (scenario multiplier)1 Parallel up 1.22 Parallel down 0.83 Steepener 0.84 Flattener 1.25 Short rate up 1.26 Short rate down 0.8
TABLE 6: Parameters u for the standardised scenarios to calculate the term deposit early redemption rate.
The standard IRRBB procedure for theseproducts starts with the assessment of the base-line conditional constant prepayment rate foreach portfolio of homogeneous loans, denotedas CPRp
0,c. It is possible to have also a non-constant prepayment rate, associated to eachtime tk, and that can be denoted as CPRp
0,c(tk).The calculation approach for this initial parame-ter is decided autonomously by the bank, andsubject to the approval of the national supervi-sor.
Once the baseline rate has been computed,the prepayment rate for each standardised sce-nario i is obtained as
CPRpi,c = min [U+2061][1, giCPRp
0,c]. (19)
The g multiplier is determined for each scenarioin the table shown in Figure 5: as intuitively ex-pected, scenarios that shift downward interestrates will imply a higher prepayment risk, andtherefore a higher multiplier for the CPR.
From the value of the prepayment rate onall portfolio-scenario-currency triplets, the bankwill then compute the expected cash-flow struc-ture, slotting each flow on the appropriate timebucket (or time bucket midpoint) in Figure 4.Given the scenario i on portfolio p denominatedin currency c, the cash-flow series on subsequenttime buckets is given by:
cfp0,c(t0, tk) = cfp,s
0,c(t0, tk) + CPRp0,c ⇥ Np
0,c(tk�1)(20)
where cfp,s0,c(tk) is the contractually scheduled
(i.e.: fixed in time tk) interest and principal pay-
ments, and Np0,c(tk�1) represents the outstand-
ing notional at the time bucket tk�1. Finally,cfp
0,c(k) is the expected total cash-flow, consider-ing the prepayment, at time tk.
For an analysis of the problems related tothe constant (or deterministic) prepayment rateapproach to deal with this type of behaviouralrisk, on which the framework above is based,see Castagna and Fede [8], ch. 9. We brieflyrecall here that this approach does not allow toexactly price the embedded optionality and toeffectively manage it, since both interest ratesand the prepayment rate are not modelled asstochastic variables; it simply allows to modifythe amortisation schedule to take into accountthe acceleration due to the prepayment choicesby the Bank’s clients, without a proper quantifi-cation of the behavioural option and its link tothe future evolution of the market rates.
Differently from the NMD’s approach above,the conditional prepayment rate is dependenton the level of market rates, so that the amortisa-tion schedule depends on each of the predefinedinterest rates scenarios. Nonetheless, since thedependence is only deterministic and the sce-narios are not defined in terms of a probabilitydistribution, not even a rough evaluation of theprepayment option is possible, withut mention-ing the fact the no Greeks can be computed fordynamic hedging purposes. A more advancedapproach, such as the one sketched in Castagnaand Fede [8], ch. 9, would consider a stochas-tic prepayment rate correlated at least with thelevel of the market interest rates, which shouldbe modelled as stochastic processes too.
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FIGURE 7: A visual summary of the Standardised Framework proposed by BIS.
iii) Fixed-Term Deposits with Early Redemption RiskThis product category should generally fall inthe “amenable to standardization” group, asusually restrictions (through penalties or evenlegal impediment) are applied on the possibil-ity for the customer to withdraw the depositedfunds earlier than contractually agreed. In thisgeneral case, expected cash flow can be con-sidered fixed and slotted into the time bucketclosest to each payment date.
Whenever the above restrictions are not spec-ified in the deposit contract, an option arises tothe customer to substantially alter the cash-flowstructure of the contract. As in the earlier caseof loans that can be paid back earlier than thecontract schedule, the bank firstly organises thewhole product group subdividing it into ho-mogeneous portfolios for each currency. Then,a baseline term deposit early redemption rateTDRRp
0,c for each currency c is computed, andused to obtain the rate for each scenario i bymeans of the formula:
TDRRpi,c = min [U+2061][1, ui ⇥ TDRRp
0,c](21)
where the u multiplier is given by the table inFigure 6.
Unlike the loan case, all cash flows deriv-ing from deposit contracts that are exposed toearly redemption risk, have to be slotted in theovernight time bucket. Therefore, the relevantcash flow structure for this procedure is deter-mined by:
cfp0,c(t0, t1) = TDp
0,c ⇥ TDRRpi,c (22)
where TDp0,c is the outstanding amount of de-
posits of type p, at the reference date. The re-maining fraction of the deposit is slotted in thetime bucket corresponding to the expiry of thedeposit.
Positions less amenable to standardisation:automatic interest rate options
Automatic options embedded in fixed and float-ing rate contracts are treated separately fromthe other categories. All interest rate optionswhich are sold to customers have to be includedin the calculations, and the bank can choose to
either include all bought options or only theones bought to hedge pre-existing short posi-tions. The choice offered to banks can be sensi-ble under a risk management angle, since dis-regarding bought options does not make therisk measurement less prudential.23 Under amanagerial point of view, missing the sensitiv-ity due to the long options in the banking bookportfolio is not reasonable.
The risk measure for this category comes inthe form of an add-on which is added to theECnao
i,c , which is defined below. For each soldoption o, the value of the change DFVOo
i,c iscomputed as the difference between:
• an estimate of the value of the sold option,given the interest rate curve in scenarioi and currency c and an increase of theimplied volatility of 25% (we assume thisincrease is in percentage with respect tothe initial implied volatility, not absolute),
and
• an estimate of the value of the sold option,given the interest rate curve in scenario iat the reference date t0.
Similarly, for each bought option q, the bankwill calculate the change DFVOq
i,c as the differ-ence in value between the option reevaluatedin scenario i for currency c, and its value at thereference date.
The total risk measure for automatic optionis given by:
KAOi,c =O
Âo=1
DFVOoi,c �
Q
Âq=1
DFVOqi,c (23)
where O and Q is the total number of optionssold, respectively bought, by the bank.
Calculation of Standardised EVE Risk Mea-sure
Up to now, we have only described the prelim-inary procedures up to cash flow slotting, forpositions that are amenable and not amenableto standardization. This because for the thirdcategory, consisting of positions less amenableto standardization, there is a separated process
23This statement is true when one looks at the terminal pay-off of the bought options, that can be either positive or nil, butnever negative. If the mark-to-market of the options is considered, clearly also long options can suffer negative variations, sothat perhaps the choice to exclude bought options should always be foregone.
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Banking Book
that does not prescribe any slotting, and thatdoes not result in a direct calculation of DEV.Therefore we will now show the sensitivity cal-culation for these two first product categories,and then conclude on the remaining one.
For each currency c (which, we recall, musthave a material exposure in the banking book)and scenario i, all notional repricing cash flowsslotted in the same bucket or bucket midpointtk are netted together, thus forming a single ag-gregated cash-flow on each node of the termstructure. To each cash-flow, a discount factoris then assigned based on the shocked interestrate curve.
Since in each scenario i the term structure ofinterest rates is given, we can assume that thediscount factor for a time bucket k, for currencyc, is given by:
Di,c(t0, tk) = e�Ri,c(tk)(tk�t0).
As we have discussed above, the rate curve usedto discount must be representative of a risk-freezero coupon rate, such as the Eonia swap ratecurves.
The Economic Value of Equity under eachscenario i and currency c is then obtained sim-ply as the sum of the discounted expected cashflows. In the standardised framework, firstlythe EV is computed without considering theautomatic interest rate options:
EVnaoi,c =
K
Âk=1
cfi,c(t0, tk)Di,c(t0, tk) (24)
After calculating the interest rate sensitivi-ties for all categories of the banking book prod-ucts, the final standardised risk measure is ob-tained by all the different EVs.
Firstly, a DEV measure is obtained for allscenario-currency pairs as follows:
DEVi,c = EVnao0,c � EVnao
i,c + KAOi,c (25)
It is worth noting that the DEV is computedwith the reverse sign, so a positive value meansa loss in the scenario.
The standardized EV risk measure for IR-RBB, which we denote as DT
STDEV, is given bythe maximum, over the six scenarios, of sum ofall positive DEV in each currency c:
DTSTDEV = max
i2{1,2,...,6}
⇢max
0; Â
c:DEVi,c>0DEVi,c
��
(26)Formula (26) is the one given in the BIS doc-ument: the max operator within the bracketsseems to be redundant, but it does not causeany problem.
A visual summary of the standardisedframework is in Figure 7.
Conclusion
The analysis that we have presented aims atfleshing out possible problems arising from astrict, or simplified, application of the frame-work outlined by the Basel Committee in thedocument [3].
We have also touched the CSRBB, which ismentioned a few times in the document [3],without providing though an explicit guidanceabout its implementation by banks. It is beyondthe scope of this work designing a full-fledgedIRRBB-CSRBB framework, so we did not inves-tigate how to soundly measure and monitor thebasis and credit risk, both in our opinion in-cluded under the same umbrella of the CSRBB.Notwithstanding this lack of analysis, we gavesome indications on how to properly calculatethe expected future cash-flows, and implicitlyindicating how the basis and credit spread fac-tors may enter into a more encompassing frame-work.
Even if it seems that the CSRBB is not es-sential for regulatory compliance, given theprescriptions in the BIS document [3], a moresound and general IRRBB-CSRBB framework isstill worth being designed and implemented forBank’s internal managerial purposes. But thisis the subject of separate research.
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References
[1] Basel Committee on BankingSupervision Principles for theManagement and Supervision ofInterest Rate Risk. 2004. Availableonline at: http://www.bis.org.
[2] Basel Committee on BankingSupervision Interest rate risk in thebanking book, Consultative Document.2015. Available online at:http://www.bis.org.
[3] Basel Committee on BankingSupervision Interest rate risk in thebanking book. 2016. Available onlineat: http://www.bis.org.
[4] Bessis, J. Risk Management inBanking. Forth edition, John Wiley& Sons. 2015.
[5] Castagna, A. Funding, Liquidity,Credit and Counterparty Risk: Linksand Implications. Iason researchpaper. 2011. Available online at:http://iasonltd.com/.
[6] Castagna, A. Towards a Theory ofInternal Valuation and TransferPricing of Products in a Bank:Funding, Credit Risk and EconomicCapital. Iason research paper. 2013.Available online at:http://iasonltd.com/.
[7] Castagna, A. and Cova, A. andCamelia, M. Modelling of Libor-OisBasisl. Iason research paper. 2015.Available online at:http://iasonltd.com/.
[8] Castagna, A. and Fede, F.Measuring and Management ofLiquidity Risks. Wiley. 2013.
[9] Castagna, A. and Scaravaggi, A.A Benchmark Framework for NonMaturing Deposits: An Applicationto Public Data Available from Bancad’Italia. Argo, n. 12. Winter 2018.
[10] Choudry, M. Bank Asset andLiability Management. Strategy,Trading, Analysis. John Wiley &Sons. 2007.
[11] Choudry, M. An Introduction toBanking Liquidity Risk andAsset-Liability Management. JohnWiley & Sons. 2011.
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In the previous issue
Issue N. 13 - 2018
ARGONew Frontiers in Practical Risk Management
1
aaaa
Spring 2018
Trading Book
Synergies and challenges in theimplementation of Basel IV regulations
SA-CCR: Implications and Challenges ofthe New Regulation
Stress Test
Modelling Banking Commissions:Application to the Italian Banking System
Last issues are available at www.iasonltd.com/research/
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