59
Issue N. 13 - 2018 ARGO New Frontiers in Practical Risk Management
Issue N. 13 - 2018
ARGONew Frontiers in Practical Risk Management
1
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 13Published in June 2018First published in October 2013
Last published issues are available online:http://www.iasonltd.com/research
Front Cover: Silvio Lacasella, Grande Cielo, 2016.
Copyright c�2018Iason Consulting ltd. All rights reserved.
New Frontiers in Pratical Risk Management
Editors:Antonio CASTAGNA (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 CASTAGNALuca OLIVOMassimo GUARNIERIMassimiliano ZANONI
Iason Consulting ltdRegistered Address:120 Baker StreetLondon W1U 6TUUnited Kingdom
Italian Address:Piazza 4 Novembre, 620124 MilanoItaly
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 five core sections are ALM & IRRBB, Credit, Trading book, Stress Test and AdvancedTechonology. Within these five macro areas, articles can be indicatively, but not exhaustively,related to models and methodologies for market, credit, liquidity risk management, valuationof derivatives, asset management, trading strategies, statistical analysis of market data andtechnology in the financial industry. All articles should contain references to previous literature.The primary criteria for publishing a paper are its quality and importance to the field offinance, without undue regard to its technical difficulty. Argo is a single blind refereedmagazine: articles are sent with author details to the Scientific Committee for peer review. Thefirst editorial decision is rendered at the latest within 60 days after receipt of the submission.The author(s) may be requested to revise the article. The editors decide to reject or accept thesubmitted article. Submissions should be sent to the technical team ([email protected]). LATEXor Word are the preferred format, but PDFs are accepted if submitted with LATEX code or aWord file of the text. There is no maximum limit, but recommended length is about 4,000 words.If needed, for editing considerations, the technical team may ask the author(s) to cut the article.
Copyright c�2018Iason Consulting ltd. All rights reserved.
Argo Magazine
Issue n. 13 / 20183
New Frontiers in Pratical Risk Management
Table of Contents
Editorial p. 5
Trading Book
Synergies and challenges in theimplementation of Basel IVregulationsBeatrice Bianco and Michele Romanini
About the Authors p. 7Description of the regulations p. 8Comparison of the regulations p. 16Conclusions p. 24References p. 25
SA-CCR: Implications andChallenges of the New RegulationLorena Corna
About the Authors p. 27SA-CCR: general overview p. 28Risk Framework p. 30Mapping of derivative transactions p. 34Conclusions p. 35References p. 37
Stress Test
Modelling Banking Commissions:An Application to the ItalianBanking SystemAntonio Castagna and Federico Mondonico
About the Authors p. 39Introduction p. 40Methodology p. 41Applications of the Framework p. 43Conclusion p. 48References p. 49Appendix p. 50
4www.iasonltd.com
Editorial
Dear Readers,
In December 2017, European Banking Authority issued a discussion paper onthe implementation of the revised market risk and counterparty risk frameworksin the European Union.
Iason was glad to have the opportunity to comment on this discussion paperand took advantage of this to examine in depth the Basel IV regulations on marketrisk and counterparty risk frameworks, contributing to Committee work.
The Trading Book section in Argo’s summer issue was inspired by this work,indeed the authors analyse the Basel IV regulations and the related committee’sproposals, following the path drawn by Gianbattista Aresi and Luca Olivo inprevious issues (“The Fundamental Review of the Trading Book StandardisedApproach for Market Risk: Revision and Challenges” and “The Effects of FRTBin the CVA Risk Framework” issued in Argo n.11 and Argo n.12, respectively).
In particular, within the first article “Synergies and challenges in the imple-mentation of Basel IV regulations” the authors propose a comparison betweenthe revised FRTB-SBA, CVA and SIMM highlighting the potential challengesthat a bank can face in implementing the new regulation. Moreover they identifypossible synergies between the regulations which permit interested parties tobenefit in their implementation, with potential economic savings.
In the second paper “SA-CCR: Implications and Challenges of the New Reg-ulation” the author discloses a general overview of SA-CCR framework focusingthe attention on European Banking Authority’s proposal on the corrections tosupervisory delta and the mapping of derivative transactions to risk categories,looking into future possibilities.
Finally, in the Stress Test section we propose you a relevant contribution onbank balance sheet by Antonio Castagna and Federico Mondonico: the studyfocuses on modelling banking commissions in the econometric field, introducingan innovative procedure based on a Bayesian approach to overcome it.
We conclude, as usual by encouraging the submission of contributions for the nextissue of Argo to help improve and innovate this newsletter everytime. Detailedinformation on how to contribute is on the front pages.
Enjoy your reading!
Antonio CastagnaLuca Olivo
Giulia Perfetti
Issue n. 13 / 20185
TradingBook
Synergies and challenges in theimplementation of Basel IV regulations
Argo Magazine
About the Authors
Beatrice Bianco:Project Manager Organization.Covering the role of PMO, she’s currentlyhelping in the developments and on-going or-ganization of the projects related to the RiskIT functions of one of the major pan Europeanbanks. Starting from an academic financialbackground, try to give a deep analysis of thequestions and issue arising from the projectsand help in the coordination between differ-ent stakeholders are her task.
Email: [email protected]: https://goo.gl/9vZ6JP
Michele Romanini:Business Analyst.As Business analyst he currently works withinthe Risk IT dedicated team of a pan-europeanbank dealing with the structuring of deriva-tive pricing models and computation of riskfigures.
Email: [email protected]: https://goo.gl/W75nLn
Issue n. 13 / 20187
Trading Book
Synergies and challenges inthe implementation ofBasel IV regulations
aaaa
Bianco Beatrice Michele Romanini
D ue to the need for all European banks to comply with the upcoming regulatory frameworks issued byBCBS and ISDA authorities, the authors decided to analyze three of the most impacting regulationsfor the bank Risk IT function. The recent regulatory need to have a more risk-sensitive framework
translated into the design of quite refined methodologies also for standardized approaches: considering thesensitivity-based common approach, the authors chose to focus on the FRTB-SBM, SIMM and SA-CVAregulations and to give a representation of the workflow needed for the metric calculation. The article hasthe intention to find all relevant similarities and synergies, both on a methodological and technical point ofview, that can be exploited by banks, as well as to warn against some challenges that can arise from theirimplementation.
IN this article we want to give a better un-derstanding of the latest regulations, pub-lished by the Basel Committee and ISDA,
that will impact the Capital Requirement cal-culation for all banks. We decided to focuson FRTB–SBM, SIMM and SA–CVA regulationsbecause they have to be implemented in theforthcoming years, their implementation willrequire a relevant computational effort, espe-cially small and medium-sized banks will facethe most significant challenges, and finally butnot for importance, because they share someimportant common features.In the first chapter we give a brief overviewof the regulatory framework of the above cap-ital requirements, with the specific rules anddefinition of the product perimeter affected bythe new rules. The second chapter is dedicatedto the comparison of the three workflows, thathave been split in three main phases, followingthe general wisdom: risk factor identification,net sensitivities calculation and metrics calcula-tion.Our aim is to highlight possible challenges thatbanks will have to cope with in the compliancewith the new regulations and also to find somesynergies across the three frameworks that can
be exploited during the implementation phase.
Description of the regulations
In this chapter we outline, for each regula-tion, the framework proposed by the regula-tors. More specifically we focus on workflows,perimeters, inputs and results that distinguishthe different prudential rules.
Overview of FRTB-SBM capitalcharge
The Sensitivity Based Method (SBM) is oneof the three new market risk frameworks in-troduced by the Basel Committee on BankingSupervision (BCBS) in January 2016 [3]. Thisframework focuses on the market risk (TradingBook PL due to the change in market prices)and it is based on the aggregation of net sensi-tivities of the risk factors the bank is exposedto.The other two charges that complete the FRTBStandardised Approach framework are the De-fault Risk Charge (introduced to capture pure
8www.iasonltd.com
Argo Magazine
default risk and Jump–to–Default exposure)and the Residual Risk Add–On (additionalrisk charge for exotic underlying risk and otherresidual risks not included in SBM and DRC).Banks can also create their own internal modelfor capital requirement calculation by followingthe FRTB-Internal Model Approach framework.
With respect to Basel II.5 rules, the revisedSBM aims to be a more risk–sensitive approachin order to give a credible fallback for tradingdesks not eligible for IMA and an appropriatestandard for banks that don’t implement aninternal model.
In the SBM framework there are three RiskCharges that need to be computed and summedup in order to calculate the final Capital Re-quirement:
1. Delta: risk measure calculated for all in-struments in the Trading Book based onthe price sensitivity to a change in thederivative underlying;
2. Vega: risk measure calculated for all in-struments with optionality based on theprice sensitivity to a change in the deriva-tive implied volatility;
3. Curvature: risk measure calculated for allinstruments with optionality that takesinto consideration the incremental risk notcaptured by Delta Risk Charge based ontwo stressed scenarios.
More specifically, all the instruments whosepayoff cannot be written as a linear functionof the underlying or instruments with option-ality are subject to Vega and Curvature RiskCharge (e.g. call, put, cap, floor, swaption,barrier/convertibility/prepayment option . . . ).The optionality might impact also RRAO frame-
work.
Net sensitivities for each Risk Charge aredivided into 7 Risk Classes and grouped intobuckets by common features. Risk Classes arethe usual asset classes and, according to FRTBnaming convention, they are: General InterestRate Risk (GIRR), Credit Spread Risk for nonsecuritization (CSR non-sec), Credit Spread Riskfor securitization (CSR sec), Credit Spread Riskfor securitization and correlation trading portfo-lio (CSR sec CTP), Equity Risk, Commodity Riskand FX Risk. A synthetic picture is reported inFigure 4.
After the risk factor identification and asso-ciation, the calculated metrics have to be aggre-gated and an hedging benefit is recognized inthis process: sensitivities are multiplied with aRisk Weight and aggregated with two correla-tion matrices given by the regulator. The firstaggregation involves the sensitivities withinthe same bucket and the second aggregationtakes in to account different buckets of a singleRisk Charge. Figure 1 represents all the stepsof the workflow with a specific focus on thefirst bucket of IR Delta; other buckets and riskcharges follow a similar workflow.
Furthermore, with the calculation of three Cap-ital Requirements, the risk that correlationbetween assets may change during a financialcrisis must be taken into consideration. For thisreason Delta, Vega and Curvature are basedon different correlation scenarios: the first sce-nario is defined as the regulatory prescribedcorrelation matrices, in the second scenariothe prescribed correlations are multiplied by afactor of 0.75 and in the third scenario the pre-scribed correlations are multiplied by a factorof 1.25 capped at 100%.
Issue n. 13 / 20189
Trading Book
The Basel Committee issued on March 2018[5] a draft revision of the Standardised Ap-proach for FRTB-SBM, in this paper the Commit-tee wants to share the revisions that will impactFRTB-SBM regulation version of 2017. Enhance-ments involve FX liquid pairs, methodology forcalculating low correlation scenario matrix andCurvature Risk Charge calculation.Concerning FX liquid pairs, triangulation of liq-uid pairs can be considered itself a liquid pairin the FX Risk Class; for example USD/EURand USD/BRL are in the list of liquid pairs soalso the triangulation EUR/BRL is considered aliquid pair too.The Basel Committee proposed a new methodol-ogy for calculating the low correlation scenariobecause it observed that, for risk factors thathave high correlations with no regard to marketconditions, the low correlation scenario tends tounderestimate the empirical correlation.Curvature Risk Charge calculation has beenchanged in order to improve the following twoaspects: the cliff effect (an abrupt increase inthe capital charge that happens if both up anddown stress scenarios are negative, due to thealternative specifications that banks must apply)and the approach to apply stressed scenarios(the capital requirement will not be calculatedon the worst stressed scenario because it canlead to two financial instruments very closelyrelated having the capital requirement calcu-lated on opposite stressed scenarios).The last changes prescribed by the regulationare different risk weight that have to be appliedto GIRR sensitivities. In this draft there are alsotwo open points for the Curvature Risk Chargeconcerning how to avoid the double countingfor FX Curvature Risk and the possibility not toapply stressed scenarios at bucket level but at’sector’ level, where sectors are specific subsetsof buckets.
Overview of SIMM
The Standard Initial Margin Model (SIMM)is the new model for calculating the initial mar-gin for non–cleared OTC derivatives, publishedby ISDA in December 2017 [6]. This new modelis aimed to update the previous recommenda-tions issued on March 2015 by the WorkingGroup on Margin Requirements composed byBCBS and IOSCO [2], where they proposed twoalternative methods for the calculation of theInitial Margin: the Standard Approach Scheduleor an approved Initial Margin Internal Model.As well as FRTB–SBM, also SIMM uses sensitiv-
ities as inputs for the aggregation formulae andit recognizes some hedging and diversificationbenefits.
The purpose of these models is to setcommon and minimum standards for MarginRequirements for non-centrally cleared OTCderivatives that are supposed to be subject tohigher capital requirements after 2007 financialcrisis. Margin requirements are divided in twotypes: Variation and Initial Margins.Variation Margin is a variable margin paymentmade by the Out-of-The-Money counterparty tothe In-The-Money counterparty in order to pro-tect the ITM counterparty from an unexpectedloss due to a default of the OTM counterparty.With this protection against the default of theOTM counterparty, the ITM counterparty willbe able to replace his positions without anyloss. Collateral has to be posted on a dailyfrequency and it is the difference between theMark-to-Market of the netting set adjusted bythe haircut and the Variation Margin alreadyposted. Mark-to-Market of the netting set isthe sum of the Mark-to-Market of the trades(the cost of replacing the trade at current mar-ket prices) with a single counterparty that aresubject to a legally enforceable bilateral nettingagreement. Eligible collateral can be cash ornon-cash assets (gold, government/corporatebond or equity) according to regulation. Postedcollateral can be reused, re-hypothecated and itdoesn’t need to be segregated.Initial Margin protects the non-defaultingcounterparty against losses that may occurif replacement costs of the instruments arehigher than the Variation Margin posted. Thislosses will happen if the Mark-to-Market of thenetting set of the non-defaulting counterpartyhas increased since the last posting of VariationMargin and if there is a timing delay betweenthe default and the actual closing out of thenetting set. The closing out of the netting setis the claim of the non-defaulted counterpartybased on the net value of all the trades. Asound model for Initial Margin must be able toestimate a distribution of losses due to futurechanges in the value of the Mark-to-Market ofthe netting set and the collateral during theMargin Period of Risk (the time between thelast Variation Margin collateral posting and theclosing out of the position). This model shouldalso take into consideration the volatility of theMark-to-Market and the possible impacts thatthe default may have on liquidity and othermarket risk factors. Initial Margin posting is
10www.iasonltd.com
Argo Magazine
a two-way collateral and follows a ’defaulterpays’ principle: each counterparty post to theother a given collateral; in case of default ofone institution, the other counterparty will re-ceive back the collateral posted. The collateralreceived plus the collateral already held will beused in order to cover the losses that may occur.Collateral posted can be cash or non-cash assetsbut it must guarantee an immediate access tothe non-defaulting counterparty, so it can’t bereused or re-hypothecated.
The workflow of the SIMM metric is similarto SBM’s one and can be divided into the samelogical steps: risk factor identification, metriccalculation and metric aggregation.
In the case of SIMM, 6 Risk Classes are iden-tified: Interest Rate, Credit Qualifying, Creditnon Qualifying, Equity, Commodity, FX. Asfor FRTB-SBM, these Risk Classes have thepurpose of identifying and classifying relevantrisk factors. In addition, a further level of clas-sification is introduced with the purpose ofassigning each trade to a single asset class. Tothis end, four Product Classes are identified:RatesFX, Credit, Equity or Commodity. Withineach product class, the six risk classes taketheir component risks only from trades of thatproduct class, e.g. Interest Rate risks for eq-uity derivatives (associated to Equity productclass) will be kept separated from Interest Raterisks for IRS derivatives (associated to RatesFXproduct class). Inside each risk class, tradesare classified into buckets following commonfeatures. In Figure 4 there is a recap of RiskClasses with associated metadata, risk weightsand correlations, while the aggregation work-flow is summarized in Figure 2.
After the association of metadata to riskfactors, net sensitivities for each trade are cal-
culated for Delta, Vega, Curvature and BaseCorrelation Margin:
• All trades are subject to Delta Margin inorder to capture the linear sensitivity to achange in the derivative underlying;
• Option–based derivatives or instrumentssubject to optionality are subject to addi-tional Vega Margin and Curvature Margin,those requirements take in considerationthe linear and non-linear sensitivity to achange in the implied volatility of the op-tion;
• Instruments that are influenced by correla-tion between defaults of different creditswithin an index (e.g CDO tranches) arealso subject to Base Correlation Margin(in the SIMM framework, the Base Corre-lation Margin is applicable only to CreditQualifying risk class).
Net sensitivities are scaled with a risk weightand a concentration factor before starting thedouble aggregation: the first aggregation in-volves sensitivities for the same bucket andthe second aggregation involves buckets for thesame Delta/Vega/Curv/BaseCorr Margin forone risk class; both aggregations use correlationmatrices prescribed by the regulator.The Initial Margin for a single risk class is thesimple summation of the specific Delta/ Vega/Curv/ BaseCorr Margins. The six Initial Mar-gins (one for every risk class) must be aggre-gated by using a third correlation matrix in or-der to calculate SIMM for each single productclass.The simple summation of the four product classSIMMs gives the final SIMM. An additionalmargin can be incorporated for notional–basedadd–ons for specified products and/or multipli-ers to the individual product class SIMM Mar-gins.
Issue n. 13 / 201811
Trading Book
FIGURE 1: We here provide a graphic description of the workflow representing the various steps needed to calculate thefinal capital requirement according to the FRTB-SBM regulation. The focus has been put on the IR Delta, but the processis analogous for the other Risk Types.
12www.iasonltd.com
Argo Magazine
Overview of SA-CVA capital charge
The Credit Value Adjustment (CVA) is theadjustment of the fair value of derivatives1 andsecurities financing transactions (STFs) in or-der to take into account the downgrade of thecounterparty quality and the shifts in relevantmarket risk factors2. Since the introduction ofBasel III a bank is in fact obliged to set apartcapital for the risk of market-to-market lossesin the expected counterparty risk of the OTCderivatives which, together with the SFTs, arethe target of the regulatory framework of theCVA.The Basel Committee in 2015 [4] started animportant review of the CVA risk frameworkwhich has been finalized in December 2017[1] with the publication of the new Basel IIIstandards. This updated version suggests anew approach for CVA capital charge that ismore consistent with the revised frameworkfor market risk (FRTB), whose application willbe enforced starting from January 1st, 2022 forboth of the aforementioned regulations3.
In order to be authorized to apply the SAmethod, banks need to meet some eligibilitycriteria: the ability to model exposure and tocalculate CVA and CVA-sensitivities to the rele-vant market risk factors, the presence of a robustmethodology to approximate the credit spreadsfor illiquid counterparties, and the existence ofa dedicated CVA desk responsible of CVA riskmanagement and hedging.
The frequency of the capital charge cal-culation is at least monthly and on demand.The framework of the final revision could besummed up in three main directions:
1. Enhance risk sensitivities taking into ac-count also the underlying market risk fac-tors in the exposure component and itsassociated hedges;
2. Strengthen robustness removing the pos-sibility of using an internal model andleaving space to only three alternatives inthe CVA capital charge computation: SA-CVA, BA-CVA and a less computational
intensive method for all the banks whichhave an aggregated notional amount ofnon-centrally cleared derivatives less thanor equal to 100 billion which consists insetting the CVA bank capital equal to 100%of the bank’s capital requirement for CCR.
3. Improve consistency with the revisedFRTB framework.
In order to have the supervisor approval touse the SA-CVA for the capital charge, the CVAmust be calculated at a counterparty level asthe expectation of the future loss resulting fromthe default of the counterparty assuming thatthe bank itself is default-free (therefore, onlyunilateral CVA is considered in contrast to Ac-counting CVA) and, furthermore, it must becalculated making use of the following inputs:
• The term structure of market-implied PD;
• The market-consensus ELGD4;
• The path of discounted future exposures5.
Regarding the calculation of the capitalcharge, the main principles that banks strictlyhave to follow are:
• The use of six asset classes (Interest rate,Foreign Exchange, Counterparty CreditSpreads, Reference Credit Spread, Equity,Commodities);
• To perform the sum of the delta and vega(for which the Counterparty Credit Spreadis not taken into account) risk calculatedfor the entire CVA book in order to havethe overall CVA capital requirement;
• In case of index hedging instruments, thecalculation of the sensitivities to all riskfactors upon which the index depends, ismandatory
The SA-CVA uses as input the sensitivityof regulatory CVA to both counterparty creditspreads and market risk factors.
Six risk asset classes are defined as rele-vant: Interest Rate (IR), Foreign Exchange (FX),Counterparty Credit Spreads, Reference Credit
1Except the derivatives transacted directly with a qualified central counterparty.2The market risk factors sensitivity has been introduced by the Basel Committee in the paper ”Basel III: Finalizing
post-crisis reforms”, Dec, 2017.3In the first consultative paper, the BCBS suggests three different frameworks: the internal model approach (IMA-CVA),
the standardized approach (SA-CVA) and the basic approach (BA-CVA) for all those banks who don’t match the eligibilityconditions for the first methods. Since the IMA-CVA has been removed by the BCBS in a consultative paper published in2016, the SA-CVA is the most refined method a bank can adopt.
4The same used for credit spreads risk-neutral default probabilities5Computed as the pricing of the derivatives transactions related to that counterparty based on simulated paths for their
relevant market risk factors
Issue n. 13 / 201813
Trading Book
Spread, Equity and Commodity. Details for therisk factor mapping and associated metadata foreach asset class are defined in Figure 4. Deltaand Vega sensitivities have to be calculatedfor these risk classe. The capital requirementfor delta risk is given by the sum of the deltacapital requirements for all the six asset classes.The capital requirement for vega risk is givenby the sum of the vega requirements for onlyfive asset classes (Counterparty credit spread isexcluded).
The workflow can be summed up in the fol-lowing steps. Net sensitivities for each Risk
Charge are divided into 6 Risk Classes andgrouped into buckets according to the featuresof the risk taken into account. After risk fac-tors identification and association, the calcu-lated metrics have to be aggregated as explainedin Figure 3 and an hedging benefit is recog-nized to the CVA portfolio only for those prod-ucts who respect the eligibility criteria. TheDelta and Vega sensitivities are multiplied for aRisk Weight, which is usually different for eachbucket; after that, they are aggregated takinginto account, first, intra-bucket correlation pa-rameters and, then, across-bucket correlationsset by the regulators.
14www.iasonltd.com
Argo Magazine
FIGURE 2: In this Figure we provide a graphic description of the workflow of the SIMM aggregation. The focus is on theBucket 1 of the IR Delta, but the process is analogous for other buckets and risk charges.
Issue n. 13 / 201815
Trading Book
Comparison between FRTB –SBM, SA – CVA and SIMM
capital charges
The aim of the second chapter is to comparethe three regulations described above, in orderto identify the synergies and the challenges thata bank has to cope with during the implementa-tion phase. The first common feature among allthe regulations is that the workflow can be splitinto three steps which share the same logic: riskfactors identification, net sensitivities calcula-tion and metrics aggregation. The first phasehas the highest level of synergies, while the sec-ond one presents the most important challengesfor the implementation of the regulations. Ithas to be highlighted that in FRTB–SBM andSA–CVA schemes there is the possibility forsmall banks or banks with a smaller tradingactivity, to opt for a reduced regulation.In the following paragraphs, we will highlightsynergies and challenges among FRTB–SBM,SA–CVA and SIMM regulations, for each oneof the above mentioned phases.
Risk Factor IdentificationWe identify the two following relevant syn-
ergies:1. Regulatory workflow is common as the
banks must always identify the Risk Fac-tors and associate metadata to them inorder to implement the bucket classifica-tion;
2. The hierarchy used for the risk factor clas-sification has a common structure amongregulations.
The first synergy concerns the common work-flow, for which the bank must be able to:
• Identify the set of Risk Factors to whichit’s exposed;
• Isolate the specific perimeter involved foreach regulation:
– The entire Trading Book and theCommodity/FX positions of theBanking Book for FRTB–SBM;
– All the non–centrally cleared deriva-tives, SFTs and CVA eligible hedgesfor SA–CVA;
– All the non–cleared OTC derivativesfor SIMM;
• Associate metadata in order to classify theRisk Factors into individual buckets.
Some peculiarities are:
• In the SA–CVA framework, the bank mustestimate the credit spreads for illiquidcounterparties from quoted spreads;
• In the SIMM framework the bank has alsoto associate single trades of each ProductClass to the Risk Classes that affect thetrade.
The second synergy involves the hierarchy ofthe classification, which, generally speaking, isstructured in the classical five risk macro–areas:Interest rate risk, Credit risk, Equity risk, Com-modity risk and FX risk. However, some dif-ferences are present at the detail level. Themost relevant difference regards the Creditmacro–area:
• In the FRTB–SBM, Credit risk is dividedin three areas, namely CSR non securiti-sation, CSR securitisasion non correlatedportfolio and CSR securitisation correlatedtrading portfolio;
• In the case of CVA, the sub-areas of Creditrisk are counterparty credit spread (thecredit spread for the derivative’s coun-terparty) and reference credit spread (thecredit spread that drives the market valueof the derivative);
• In the SIMM case, the division is simi-lar to the FRTB–SBM one and the areasare Credit Qualifying (approximately CSRnon securitization + securitization corre-lation portfolio) and Credit Non Qualify-ing (approximately CSR securitization noncorrelation trading portfolio).
FRTB-SBM framework prescribes the highestlevel of granularity because the perimeter im-pacted is the widest of the three regulations.Furthermore, Supervisors usually force banksto provide a deeper disclosure on market riskexposure and trading activities as it is one ofthe most common and relevant financial risksthat might deteriorate solvency of the institu-tion. On the contrary, SA-CVA has the lowestlevel of granularity because it implies the high-est computational effort.Let’s now investigate, for each Risk Class, whichare the similarities concerning the associationof metadata to Delta risk factors among all theregulations.
16www.iasonltd.com
Argo Magazine
Interest Rate
Risk factors for Interest Rate risk are defined assome specific pillars (called vertices) of the risk-free yield curves and have to be associated withtwo metadata: the type of the curve (inflation,Cross–Currency Basis or zero curve) and thecurrency of the curve. However, the requiredgranularity of risk factors is different for thethree regulations. In the FRTB–SBM framework,inflation and CCB curves are considered flat,while the zero curves must have ten vertices:0.25y, 0.5y, 1y, 2y, 3y, 5y, 10y, 15y, 20y and 30y.In the CVA framework, flat inflation curves andthe five vertices 1y, 2y, 5y, 10y, 30y for the zerocurves are considered (Cross Currency Basiscurves are not relevant in this framework). Forthe SIMM regulation, as in the FRTB-SBM, thereare flat inflation and CCB curves, but in addi-tion there are twelve vertices for the zero curves:2w, 1m, 3m, 6m, 1y, 2y, 3y, 5y, 10y, 15y, 20y and30y.
Credit
Credit macro–area is the one that shows thehighest level of differences, especially in theperimeter of the regulations: FRTB–SBM andSIMM prescribe a specific Risk Class for com-plex credit derivatives (e.g. resecuritizations,nth–to–default, ABS, . . . ) while SA-CVA hasone single framework for all credit derivatives.Nevertheless, CVA framework takes into consid-eration both the credit spreads of the counter-party and of the underlying of the credit deriva-tive. For all of the three regulations, risk factorsare represented by the credit spreads of the un-derlying curves (in case of credit plain deriva-tives and securitisations) or of the tranches (inthe case of complex derivatives). The metadatathat have to be associated to those risk factorsare credit quality (Investment Grade or HighYield/Non Rated), industry sector of the issuerand five vertices of the credit curve (0.5y, 1y, 3y,5y, 10y for FRTB–SBM and SA-CVA for counter-party credit spreads and 1y, 2y, 3y, 5y, 10y forSIMM.). There are also different rules for therisk factor identification in case the credit deriva-tive is a securitisation or a plain one. Creditquality is not a relevant metadata for counter-party credit spread in the SA-CVA framework.
Equity
For the Equity macro – area, risk factors arerepresented by equity prices and – in theFRTB–SBM framework – also by repo rates. The
metadata used for Equity products are the size(large or small, accordingly to the market capi-talization threshold of USD 2 billion), the region(emerging market or advanced economies) andfour sectors (this differentiation holds only forthose equity Risk Factors classified in the ‘large’size). FRTB–SBM and CVA frameworks havealso a residual bucket for non classifiable riskfactors, while SIMM framework has no residualbucket but two other buckets named ‘Indexes,Funds, ETFs’ and ‘Volatility Indexes’.
Commodity
Commodity Risk Factors are represented bycommodity spot prices for all the regulations.The metadata associated to the prices usedin FRTB–SBM framework are commodity con-tract grade (the minimum accepted standard forthe deliverable commodity), delivery location,time to maturity of the instrument (consideredvertices are 0y, 0.25y, 0.5y, 1y, 2y, 3y, 5y, 10y, 15y,20y and 30y) and commodity typology used forbucketization. This last metadata is commonfor all the regulations, but there are some dif-ferences in its granularity: CVA and FRTB–SBMhave 10 different buckets plus a residual bucket,while SIMM prescribes an higher degree of gran-ularity with 15 different buckets plus ‘Indexes’and a residual bucket.
Forex
FX Risk Factors are all the ccy pairs betweenthe domestic currency of the bank and the cur-rency of the derivative. The pairs need to beassociated to the list of liquid currencies (forFRTB–SBM) or to the high/medium/low volatil-ity currencies (for SIMM). Currencies withinthis lists are allowed to compute a lower sensi-tivity in order to take into account for the lowerliquidity risk. In addition to pairs cointainedwithin the list, also triangulations of those pairsare allowed to the reduced capital requirement.For example, if USD/EUR and USD/BRL are inthe list of liquid pairs so also the triangulationEUR/BRL is considered a liquid pair too.
Vega Risk factors
Vega risk factors are the implied volatilities thatenter in the pricing models of the instruments,SA-CVA also takes into account volatilities usedfor the risk factor path generation. Bucket clas-sification is similar to Delta risk factor’s one, soalso the metadata that have to be associated toVega risk factors is similar.
Issue n. 13 / 201817
Trading Book
Net Sensitivities CalculationFor a bank, this phase is the most challeng-ing one; the calculation of the metrics mustbe compliant to prescribed bumps and formu-las, furthermore the risk IT engine should beupgraded in order to handle properly highercomputational burden and increased number ofdata with respect to past regulations.The most relevant issues come from the imple-mentation of all the different metrics calcula-tions, and from the enhancement of the method-ologies and Risk IT technologies used in thispart of the regulatory process. Challenges maycome from the following aspects:
• A full sensitivity calculation workflowmust be in place; in case banks don’t haveit already they have to build a new one or,in case it’s already present, an upgrade ofthe risk engine may become necessary.
• Sensitivities coming from different LegalEntities or Front Offices need to be col-lected in a single repository.
• Data management has to be improved inorder to handle data flows containing sen-sitivities and metadata with an high de-gree of granularity.
• According to the SIMM regulation, sincebanks have multiple choices regarding theshift that has to be applied to risk factors,they should opt for the methodology thatallows them to have the most appropriaterepresentation of the risks they are subjectto;
• CVA Vega is always material so it has tobe calculated in all cases and it takes intoaccount a wider range of volatilities usedin the models, including the ones used forthe generation of simulated risk factorspaths.
All of these issues will bring a relevant effort ifa dedicated Risk engine is still not present inthe bank’s skeleton, but also banks with an up-graded Risk IT area may have to enhance theirmethodologies in order to be fully compliantwith different regulations.
Concerning the calculation of the metricsthere are substantial differences in the type andthe formulae of the sensitivities that have to becalculated, the principal differences are summa-rized in Figure 5. Let’s now examine separatelythe three frameworks.
FRTB-SBM
For FRTB–SBM the metrics that have to be cal-culated are Delta, Vega and Curvature.Delta risk is the difference between the shockedmarket value of the derivative and the currentmarket value. Prescribed shocks are alwaysupward bumps of 1bp (for interest rate curves,credit spreads and equity repo rates) or of 100bp(for equity spot prices, commodity prices andFX pairs), the difference then has to be rescaledfor the applied bumps.Vega risk is computed as the implied volatilitymultiplied for the first order sensitivity of theoption/derivative to the implied volatility itself.Those measures are calculated by the bank’s in-dependent Risk Management internal function.Curvature risk is based on a stressed upwardand downward scenario of the risk factors.Delta effect has to be removed from thesestressed difference in order to consider onlythe higher level of price sensitivity to the un-derlying. This metric is peculiar of FRTB-SBMand has no analogue in the other regulations.Moreover, it has been noted that it is more simi-lar to a stress measure than to a true sensitivity(indeed it has a meaning close to the gammabut it is defined in a different way).
SA-CVA
In the SA-CVA framework, shifts are not ap-plied to the market value of the singular deriva-tives (as it is for FRTB–SBM and SIMM), butthey are applied to the CVA exposure to eachcounterparty. This characteristic makes heav-ier/tougher the computation of the CVA netsensitivities because it implies a re-simulationof the exposures; only for CVA hedges marketvalue sensitivities have to be calculated.SA-CVA framework requires only Delta andVega sensitivities for aggregate CVA and for theeligible hedging instruments for a given riskfactor. If an eligible hedging instrument is anindex, banks have to calculate sensitivities forall the underlying risk factors of the index.Delta sensitivity has to be calculated for InterestRate, Counterparty Credit Spread, ReferenceCredit Spread, Equity, Commodity and FX riskfactors. Metrics are calculated via the appli-cation of a shift of 1bp (for Interest rate andCredit Delta risk factors) or of 100bp (for Equity,Commodity and FX Delta risk factors). Thedifference between the CVA computed with theshifted risk factor with respect to the currentCVA has then to be scaled for the bump applied.
18www.iasonltd.com
Argo Magazine
Banks can apply smaller shifts to risk factors ifdoing so they are more consistent with internalrisk management calculations.Vega sensitivity has to be calculated for allthe volatilities used in the exposure calculationmodel, both for volatilities used in the gener-ation of risk factor paths and the ones usedin the pricing models. Vega sensitivities havealways to be calculated, regardless of whetheror not the portfolio includes some options. Theformula is similar to Delta’s one: a shift of100bp has to be applied simultaneously to allthe volatilities and also here the difference inthe CVA has to be rescaled for the shift applied.
The smaller number of sensitivities requiredand the reduced granularity of risk factors (bothin terms of buckets and vertices) is therefore bal-anced with a higher computational burden. Inparticular, standard bump and run techniquesmay reveal extremely expensive in the CVA con-text. Even though precise bumps are prescribedin the sensitivity definition, BCBS states thata bank may use smaller values of risk factorsshifts if doing so is consistent with internal riskmanagement calculations: this opens the possi-bility to use alternative methodologies aimed atavoiding the iteration of multiple MC simula-tions of EPE computations. The most popularmethod at this regard is AAD (Adjoint Algo-rithmic Differentiation) which can lead to im-pressive gains in terms of computational time.The drawback is that the risk architecture wouldtypically need strong enhancements in order tohandle these kinds of techniques.
SIMM
SIMM regulation requires the calculation ofDelta, Vega, Curvature and Base Correlationsensitivities.
Delta risk is the difference of the shockedmarket value and the current one (as inFRTB–SBM framework): but shocks can beupward, downward or central of 1bp (for In-terest Rate and Credit product asset classes)or of 100bp (for Equity, Commodity and FXproduct classes); if banks use one of those threeshocks, the resulting difference is not scaled forthe applied bump. Financial institutions canalso go for an alternative option, that consist inusing a reduced bump with a rescaling of theresulting difference.
Vega risk factor calculation is similar toDelta one, with the only difference that thebump will be applied to the implied volatil-ity of the instrument. Upward, downward,central or reduced shocks are allowed heretoo. Curvature risk charge takes into consid-eration the non–linear exposure to impliedvolatility changes (therefore it has a differentmeaning with respect to the Curvature definedin FRTB–SBM framework, which is focused onnon–linear exposure to underlying changes asa stress scenario). As a consequence, sensitiv-ities calculation is based on the Vega risk factors.
Base Correlation is the difference betweenthe market value of the instrument and themarket value of the instrument where the BaseCorrelation curve/surface of the risk factor –a given credit index family – is bumped of anupward factor of 100bp. This metric has to becalculated only for Credit Qualifying Risk Class.
Banks, in case of the calculation of InterestRate Delta sensitivities, can choose between thefollowing options:
• Upward:
sx = V(x + 1bp)� V(x)
• Downward
sx = V(x)� V(x � 1bp)
• Central
sx = V(x + 0.5bp)� V(x � 0.5bp)
• Reduced scaled
sx =V(x + #1bp)� V(x)
#
where:
• sx is the sensitivity to the risk factor x;
• V(x) is the market value of the instrument,given the value of the risk factor x;
• # is a scaling factor, 0 < |#| < 1.
This choice is not present in the two other frame-works, where only upward shifts are allowed6.Banks should make a deep study of the impacton the final capital requirement given by the
6In the case of SA-CVA, however, banks have the possibility to calculate smaller risk factor bumps than the prescribedamounts, as discussed above
Issue n. 13 / 201819
Trading Book
use of different sensitivity formulae. In fact, op-tion–based derivatives may have different sen-sitivities if an upward or downward shift isapplied, due to the non linearity of their pay-
offs and the moneyness of the instrument willplay a crucial impact on the choice of the mostconvenient formula to be used.
20www.iasonltd.com
Argo Magazine
FIGURE 3: In this Figure we provide a graphic description of the workflow of the CVA aggregation. The focus is on theBucket 1 of the IR Delta, but the process is analogous for other buckets and risk charges.
Issue n. 13 / 201821
Trading Book
FIGURE 4: In this figure we compare the mapping of the risk factors for the three frameworks.
22www.iasonltd.com
Argo Magazine
FIGURE 5: In this figure we compare the most important differences in the methods for calculating net sensitivities for thethree frameworks.
Metrics Aggregation
For all the three regulations, the third phaseis based on the aggregation of the sensitivitiesaccording to predefined rules. The three frame-works share the same procedure, the only differ-ence arise in the prescribed values of correlationmatrices, in the risk weights and in other pa-rameters (i.e. concentration factors, historicalvolatility ratios, . . . ) used in the aggregationof the exposures. As a common feature, byusing correlation matrices for the aggregationof sensitivities, some hedging benefits are rec-
ognized in the calculation of the final CapitalRequirement. An important peculiarity thatcharacterizes SA-CVA is that, at the end of themetrics aggregations, the capital calculated hasto be multiplied by a factor of 1.25 in order tocompensate for the lower degree of granularityin the risk factor identification and the fact thatonly first order derivatives are taken into con-sideration. Table 1 recaps the differences amongthe three workflows with respect to the num-ber of aggregations prescribed by the regulatorand the other risks that have to be taken intoconsideration.
Issue n. 13 / 201823
Trading Book
FRTB-SBM CVA SIMM
Number ofaggregations
• Risk factors within thesame bucket;
• Buckets within the samerisk class
• Risk factors within thesame bucket;
• Buckets within the samerisk class.
• Risk factors within thesame bucket;
• Buckets within the samerisk class;
• Risk Classes within thesame Product Class.
Other risksconsidered
Risk in a change of the correlationbetween instruments ! 3 differentsets of correlation matrices are pre-scribed: High/Medium/Low Cor-relation Scenario.
Model risk (losses due to a modelthat lacks of accuracy) ! a multi-plier is applied to the aggregatedrisk charge of each Risk Class.
Concentration risk in the TradingBook ! a concentration risk factoris applied to weighted sensitivitiesbefore the start of the aggregation.
TABLE 1: In this table we highlight the major differences in the aggregation workflow across the three regulations.
Conclusion
In conclusion, the implementation of theseregulations will force banks which still don’thave in place a structured Risk workflow tohandle some difficulties.In our opinion the most important challengeswill come from the sensitivities calculation, es-pecially for SA–CVA because the CCR chainis usually less developed with respect to themarket risk one due to the recent major focuson this topic by supervisory autorithies.Taking into account all the synergies that arise
from the implementation of the regulations (i.e.common workflow, risk factors and metadata)a bank should be able to enhance the actualRisk engine with a leaner process or to create anew one exploiting all the common features inthe regulations and to avoid any duplication ofprocedures.In 2019 banks will have to be compliant to SIMMframework; once the banks create a workflowfor Risk Factor Identification, they should beable to adapt the same logic for the other tworegulations in order to meet the deadline of2022.
24www.iasonltd.com
Argo Magazine
References
[1] Basel Committee on BankingSupervision. Basel III: Finalisingpost - crisis reforms. December 2017.Available online at:https://www.bis.org/.
[2] Basel Committee on BankingSupervision. Margin requirementsfor non - centrally cleared derivatives.March 2015. Available online at:http://www.bis.org/.
[3] Basel Committee on BankingSupervision. Minuimum capitalrequirements for market risk. January
2016. Available online at:http://www.bis.org/.
[4] Basel Committee on BankingSupervision. Review of the CreditValuation Adjustment RiskFramework. July 2015. Availableonline at: https://www.bis.org/.
[5] Basel Committee on BankingSupervision. Revisions to theminimum capital requirements formarket risk. March 2018. Availableonline at: http://www.bis.org/.
[6] International Swaps andDerivatives Association. ISDASIMM Methodology, version 2.0. July2017. Available online at:http://www.isda.org/.
www.iasonltd.com25
TradingBook
SA-CCR: Implications and Challenges of theNew Regulation
Argo Magazine
About the Authors
Lorena Corna:Business Analyst.As Business analyst she currently workswithin the Risk IT dedicated team of a bigpan-European Bank. In particular, she fol-lows the backtesting model for CounterpartyCredit Risk.
Email: [email protected]: https://goo.gl/dq5yBd
www.iasonltd.com27
Trading Book
SA-CCR: Implications andChallenges of the New
Regulationaaaa
Lorena Corna
I n light of the revised regulatory frameworks for market and counterparty risks, the author gives anoverview on the Standardised Approach for Counterparty Credit Risk (SA-CCR) and its implementationissues in a bank Risk framework. The approach presented by the Basel Committee on Banking Supervision
on March 2014 required a study performed by the European Banking Authority concerning the mappingof derivative transactions to risk categories and the correction of regulatory formulas in the current contextof negative interest rates. Although the new regulation solves some shortcomings of the current standardapproach to CCR, e.g. partially recognizing netting benefits coming from margining and hedging, a fewfeatures still need particular attention in order to properly measure the risks associated to the instruments inscope of the regulation. In particular, as also pointed out by EBA, a significant impact on the final capitalrequirement (the EAD) can derive from the methodology employed to identifiy the primary risk driver of eachtransaction. After revising the methodologies proposed by EBA, a case study is presented, based on a portfolioincluding cross currency swaps, and an alternative methodology, aimed at assessing the materiality of eachrisk driver of the transaction, is proposed. The details on the latter are left to a future publication.
In March 2014, in order to substitute theCurrent Exposure Method and the Stan-dardised Method, the Basel Committee pre-
sented a new approach for measuring the expo-sure at default (EAD) named Standardised Ap-proach for Counterparty Credit Risk (SA-CCR, [1]).In scope of the proposed regulation, there areOTC derivatives, exchange-traded derivativesand long settlement transactions.The SA-CCR comes from the need to overtakethe lacks of non-internal methods: it distin-guishes margined and unmargined derivativetransactions, it recognizes some netting bene-fits, it can be easily and simply implementedand, moreover, it would reduce the discretionof banks and national authorities.The EAD, under SA-CCR, is calculated at net-ting set level and it is given by a multiple ofthe effective expected positive exposure. Thelatter is the sum of replacement cost (RC) andpotential future exposure (PFE), in formula:
EAD = a · (RC + PFE) , (1)
where a = 1.4 (as in internal model method).In order to properly consider the netting bene-fits, the Basel Committee defines the concept ofhedging set as following: A “hedging set” underthe SA-CCR is a set of transactions within a singlenetting set within which partial or full offsetting isrecognised for the purpose of calculating the PFEadd-on [1].Moreover, the Basel Committee established that,for the same netting set, the EAD for a marginednetting set cannot be higher than the EAD forunmargined netting set (paragraph 129, [1]).With SA-CCR, for each derivative transactionwithin a netting set, the bank has to determinethe primary risk factor (or factors) and assignit to one (or more) of the following five assetclasses:
• Interest Rate
• Foreign Exchange
• Credit
• Equity
28www.iasonltd.com
Argo Magazine
Add#on& Calculation
Trade&level1. Adjusted*Notional*
(for$IR$and$CR$transactions,$the$AdjNotincorporates$the$supervisory$duration)
2. Maturity*Factor*(for$margined$and$unmargined$ $transaction)
3. Supervisory*delta*adjustment
Effective*Notional
Supervisory$factor Add?on
Aggregated&level21. Hedging*set*2. Asset*class*3. Netting*set*
2 For$credit,$equity$and$commodity$ derivatives,$this$involves$the$application$of$a$supervisory$correlation$parameter$to$capture$important$basis$risks$and$diversification
FIGURE 6: General addon calculation
• Commodity
Furthermore, the European Commission pro-posed to introduce a new risk categorynamed “other risk” (article 277, [4]).
Among these risk categories, the basis transac-tions and volatility transactions represent dis-tinct hedging sets in their corresponding assetclasses with modified supervisory factors.As stated before, one advantage of SACCR isthe distinction of margined and unmarginedtransaction. This characteristic is reflected inthe calculation of replacement cost (RC).For netting sets not subject to a margin agree-ment, the replacement cost represents the lossthat would occur if counterparty default andclose-out happened immediately.If there is a collateral other than variation mar-gin, the former represents an indipendent collat-eral amount (ICA) that can be posted or receivedby the bank. Therefore, the net indipendentcollateral amount (NICA) is defined as “any col-lateral (segregated or unsegregated) posted by thecounterparty less the unsegregated collateral postedby the bank" [1]. Accordingly, for unmarginedtrades the replacement cost is given by:
RC = max{V � C; 0}, (2)
where V is current mark to market value oftransactions and C represents the net haircut col-lateral held by the bank calculated with NICAmetodology.For margined trades, the replacement cost corre-sponds to the loss when a counterparty defaultsat present or at a future time, supposing that the
close-out and replacement of transactions occurinstantaneously. As a consequence, the replace-ment cost for a netting set subject to marginagreement is calculated as following:
RC = max{V � C; TH + MTA � NICA; 0},(3)
where V and C are the same as in the un-margined case, TH is the non negative thresholdand MTA is the minimum transfer amount.The second component of EEPE is given by po-tential future exposure (PFE), which depicts theworst exposure in one year from calculationdate (in the unmargined case) or in the marginperiod of risk (in the margined case). The PFE isgiven by the product between a multiplier andan aggregate add-on component.The multiplier depends on the replacement cost:
• If RC is positive, the multiplier is equal toone;
• If RC is zero the multiplier is calculatedas following:
multiplier =min{1; Floor + (1 � Floor) ·exp A},
where A =⇣
V�C2·(1�Floor)·AddOnaggregate
⌘and
the floor is equal to 5%.
The AddOnaggregate is the sum of add-ons foreach asset class and it will be described indetail in the following section.
Issue n. 13 / 201829
Trading Book
Risk Framework
Metrics computation
The calculation of add-ons, summarized infigure 6, is the result of the methodology pre-scribed for each asset class, nevertheless someaspects are shared.Given a netting set, the first step is the com-putation of adjusted notional. This computationdepends on the asset class:
• Interest rate and credit derivatives: the ad-justed notional for a derivative transactioni is the product of trade notional in domes-tic currency and the supervisory durationSDi defined as:
SDi =exp (�0.05 · Si)� exp (�0.05 · Ei)
0.05,
where Si is the start date and Ei is the enddate of trade floored by ten business days.If the trade is ongoing, the parameter Si isequal to zero.
• Foreign exchange derivatives: the ad-justed notional is equal to the notionalof foreign leg converted in domestic cur-rency. If both legs are in foreign currency,both notionals will be converted and themaximum should be taken.
• Equity and commodity derivatives: theadjusted notional is the product of currentunit price of stock or commodity and thenumber of units referenced by the trade.
At paragraph 158 of [1] the rules to determinethe notional, if the latter is not clearly definedor it is not fixed until maturity, can be found.A maturity factor (MF) is applied to the adjustednotional; in the calculation of PFE, the differ-ence of margined and unmargined netting setis reflected on this parameter:
• For an unmargined transaction i, the ma-turity factor is given by:
MFunmarginedi =
smin {Mi; 1year}
1year,
where Mi is the maturity of transactionexpressed in years floored by 14 calendardays (i.e. 10 business days).
• For a margined transaction i, the maturity
factor is given by:
MFmarginedi =
32
sMPOR1year
,
where MPOR refers to the Margin Periodof Risk of the transaction (paragraph 164,[1]).
Moreover, a supervisory delta adjustment is ap-plied to the adjusted notional: the latter wouldreflect the direction of the derivative transactionand its non-linearity. Three cases are consid-ered:
• Options: the Basel Committee specifiesthe following formula:
d =sign · type·
· f
0
@type ·ln⇣
PK
⌘+ 0.5 · s2 · T
s ·p
T
1
A ,
where type is -1 for put option and +1 forcall option and sign is -1 for sold optionand +1 for bought option; P is underly-ing price; K is strike price and T is thelatest contractual exercise date of optionand, finally, the supervisory volatility s isspecified on the basis of risk category andthe nature of the underlying instrument(table 2).In the context of negative rates, an adjust-ment of supervisory delta formula estab-lished by Basel Committee is needed: EBAsuggests to add a l shift in above formulain order to move the interest rate insidepositive area [3]. This parameter shouldsatisfy some critical aspects: l shift de-pends on interest rate of specific jurisdic-tion and it should progressively reduceuntil zero when the interest rates becomepositive. In order to guarantee an uni-formity across the European Union, EBAproposed two options:
– l is defined with EBA RTS for eachEU currency and regularly updated;
– l is quoted on the relevant marketand therefore automatically updatedfor the pertinent jurisdiction.
Furthermore, the Basel Committee definesthe calculation of effective notional for dig-ital options in [2]: in this case the digi-tal payoff z is approximated with a collar
30www.iasonltd.com
Argo Magazine
combination of European options of thesame type (call or put) with the strikesequal to 0.95Kz and 1.05Kz. Therefore,the effective notional is separately eval-uated for all the European option of thecollar combination, thanks to the aboveformula.7
• CDO tranches: the supervisory delta ad-justment is given by
d = sign15
(1 + 14A) · (1 + 14D),
where sign is equal to +1 for purchasedCDO tranches and -1 otherwise, A is theattachment point and D id the detachmentpoint.
• Other instruments: d is equal to +1 if thetransaction is long in the primary risk fac-tor or it is equal to -1 if the transaction isshort in the primary risk factor.
The product of adjusted notional, maturity fac-tor and supervisory delta adjustment is equalto the effective notional amount. The latter is sub-ject to a supervisory factor, defined for each assetclass, in order to obtain the addon. As stated insection , for basis and volatility transaction, thesupervisory factor is multiplied by one-half andfive respectively.
Metrics aggregation
We now present the specific rules for theaddon calculation for each asset class. Onceall the add-ons at asset class level have beenobtained, the aggregated add-on is equal to thesum of asset class add-ons.
Interest rate derivatives
In this asset class, the hedging set is representedby the currency and it is split in three time buck-ets: i) maturity smaller than 1 year, ii) maturitybetween 1 and 5 years and iii) maturity largerthan 5 years. The SA-CCR recognises full offset-ting benefit within maturity buckets.Given a netting set, for each transaction i theeffective notional Djk for maturity bucket k ofhedging set j is calculated as follows:
Djk = Âi2(j,k)
di · AdjNi · MFi (4)
where di is the supervisory delta adjustment,AdjNi is the trade-level adjusted notionalamount and MFi is the maturity factor. Afterthat, bucket aggregation of the effective notionalE f f N is performed: for each hedging set j, par-tial offsetting benefit is recognized across buck-ets k = 1, 2, 3 with the following formula:
E f f Nj =h(Dj1)
2 + (Dj2)2 + (Dj3)
2 + 1.4 · Dj1·
· Dj2 + 1.4 · Dj2 · Dj3 + 0.6 · Dj1 · Dj3
i12
Nevertheless, if a bank can not admit offsetacross maturity bucket, the above formula be-come: E f f Nj = |Dj1|+ |Dj2|+ |Dj3|.After that, the add-on at hedging set level iscalculated as
AddOnj = SFj · E f f Nj.
The asset class add-on is obtained by summinghedging set add-ons.
Foreign exchange derivatives
The effective notional is calculated for eachhedging set j, represented by the currency pair,with the same formula for interest rate deriva-tives (4). The hedging set add-on is given by:
AddOnj = SFj · |Dj|,
and the asset class add-on is obtained by sum-ming hedging set add-ons.
Credit derivatives
The effective notional is computed for eachhedging set j, represented by all the credit trans-actions with the same entity, via the formula (4)and the hedging set add-on is calculated withthe formula:
AddOnj = SFj · Dj, (5)
where SFj for single name entities is definedby the reference name’s credit rating whereasfor index entities is based on index grade (i.e.investment or speculative).In order to recognize a partial offsetting amongthe entity level add-ons, a single factor model isused, where the risk of this asset class is split intwo elements:
• Systematic component, where a full offset isallowed
7The Basel Committee specifies that the absolute value of the digital option effective notional cannot exceed the ratio ofthe digital payoff to the relevant supervisory factor.
Issue n. 13 / 201831
Trading Book
• Idiosyncratic component, where no offset-ting benefit is recognized.
The degree of offsetting benefit is establishedwith the correlation factor and the asset classadd-on is then given by the following formula:
AddOn =
2
4
Âj
rj · Addonj
!2
+ Âj
⇣1 � r2
j
⌘·
·�
Addonj�2i
12 ,
(6)
where the first term is the systematic compo-nent, the second term is the idiosyncratic com-ponent and rj is the correlation factor definedin table 2.
Equity derivatives
The effective notional is calculated for eachhedging set j, represented by single names orindices, with the formula (4) and the hedgingset add-on is computed with formula (5).For each reference entity a single factor modelis used, in order to identify the systematic com-ponent (where offsetting is allowed) and theidiosyncratic component like for credit deriva-tives.The asset class add-on is given by formula (6)as well.
Commodity derivatives
For commodity derivatives, the Basel Com-mittee defines four typologies of commoditieswithin which stable meaningful joint dynamicscan be found: i) energy, ii) metals, iii) agricul-tural and iv) other commodities. However, this
categorization does not recognize the specificpeculiarities of commodities such as locationand quality: if banks reveal a significantly ex-posure to the basis risk of different productswith the proposed categorization, the nationalsupervisor can require to banks a more refineddefinition of commodities.Taking a single netting set, full offset in thesame typology of commodity and a partial off-set among four classes of commodities are rec-ognized.For trades of commodity type k in hedging setj, the effective notional is given by:
Dkj = Âi2(k,j)
di · AdjNi · MFi
Therefore, the add-on at commodity type levelis the product of above effective notional andthe proper supervisory factor definend in table2.For each hedging set, the Committe again dis-tinguishes between systematic and idiosyncraticcomponents through a single factor model. Theadd-on at hedging set level is calculated as:
AddOnj =
2
4
rj · Âk
Addonk
!2
+⇣
1 � r2j
⌘·
· Âk(Addonk)
2i
12 ,
where rjis the correlation factor for hedging setj defined in table 2. Finally, the add-on for com-modity asset class is the sum of above hedgingset add-ons.
32www.iasonltd.com
Argo Magazine
Asset Class Subclass Supervisory factor Correlation Supervisory option volatilityInterest rate 0.50% N/A 50%Foreign 4.0% N/A 15%exchangeCredit AAA 0.38% 50% 100%(single name) AA 0.38% 50% 100%
A 0.42% 50% 100%BBB 0.54% 50% 100%BB 1.06% 50% 100%B 1.6% 50% 100%CCC 6.0% 50% 100%
Credit (index) Inv. Grade 0.38% 80% 80%Spec. Grade 1.06% 80% 80%
Equity Single name 32% 50% 120%Index 20% 80% 75%
Commodity Electricity 40% 40% 150%Oil/Gas 18% 40% 70%Metals 18% 40% 70%Agricultural 18% 40% 70%Other 18% 40% 70%
TABLE 2: Table of supervisory parameters
Asset Class Hedging Set (HS) Offsetting BenefitInterest rate Currency.
Further classification into three buckets:
• maturity < 1 year,
• 1 year < maturity < 5 years,
• maturity > 5 years.
Full offset in the maturity bucket andpartial offset across buckets.
Foreign Exchange Currency pair. Full offset in the same HS, no offsetamong different HS.
Credit and Equity Single HS for each asset class. Full offset for the same entity, partial off-set among different entities.
Commodity 4 commodity categories:
• energy,
• metals,
• agricultural,
• other commodities.
Full offset for the same category, partialoffset among different categories.
TABLE 3: Summary of hedging sets for each asset class
Issue n. 13 / 201833
Trading Book
Mapping of derivativetransactions
The Basel Committee established that the al-location of derivative transactions to each assetclass is made by their primary risk driver: thelatter would be the most material risk driver ofthe transaction and should be assessed usingsensitivities and volatilities of the underlyinginstruments.Furthermore, if the derivative transaction can-not be assigned to only one risk category, thenit must be allocated to each asset class with thesame position. About this point, the EuropeanBanking Authority (EBA) suggested to define acap on the number of risk categories to whicha single derivative transaction can be allocated[3].Nonetheless, Basel Committee did not definea methodology in order to perform the map-ping of derivative transactions to risk classesand the European Commission in [4] indicatedEBA as a responsible to devise a methodologyto mapping the derivative transactions in one(ore more) risk category.In order to perform this activity, EBA suggestsa three-step approach for the identification andclassification of risk factors:
• Qualitative approach,
• Quantitative approach,
• Fallback approach.
Qualitative approach
In some cases the assessment of the materi-ality of risk drivers is simple, e.g. in the case ofderivative transactions with a single risk driveror several risk drivers referring unambiguouslyto the same risk category, or for structured prod-ucts related to a single asset class. In these cases,it is not required to outline any process for theidentification of risk factors and EBA proposeda list with the aim of mapping risk category,primary risk factor and instruments.On the other side, consider for example the caseof a cross currency swap (CCS): a priori it couldbe assigned to foreign exchange or interest rateasset classes based on the impact of the rele-vant risk factors to the exposure. Therefore, in
addition to the above mentioned list, a quantita-tive method to map transactions to asset classesshould be defined.If the CCS is assigned to the foreign exchangeclass, the previously described rules can be ap-plied in a straightforward way. Instead, if theCCS is associated to the interest rate asset class,the hedging set currency has to be defined. Inparticular, when both the legs of the CCS aredenominated in currencies other than the do-mestic currency, the logic for the identificationof the hedging set currency needs to be definedin such a way that the hedging purpose of theinstrument is correctly taken into account.In this case, the Basel Committee requires toconvert the notional amount in domestic cur-rency (paragraph 157, [1]) while computing thetrade level adjusted notional. For a cross cur-rency swap, we deem that it would be morepertinent to use the currency of the receive legas hedging set currency.In table 4 a specific example of netting set in-cluding two interest rate swaps, in EUR andUSD, together with three CCS on EUR/USD isconsidered. The transactions included in thenetting set come from a real portfolio and werechosen so that they have different maturities,typologies (payer or receiver, fix vs float or fixvs fix or float vs float) and margining details.The impact on the EAD, due to different assign-ment8 of the CCS to IR or FX asset classes, isassessed: as it can be shown applying BCBSrules to the two scenarios, the EAD change is ofthe order of 13%. This is already a significantvariation, however, since only the PFE (throughthe aggregated Add-On) affects the risk factormapping, and since the RC contribution dom-inates the EAD in our example, it is more ap-propriate to analyze the separate impact on thePFE part of the exposure. If we concentrate onthe PFE alone, we see that, for our netting setexample, the impact is of the order of 159%,with a higher PFE in the case where the CCSnumber 5 is included in the IR asset class. Thehuge impact on this kind of products, largelytraded by banks indeed, strongly indicates thata careful quantitative assessment of the mate-riality of each risk driver should be identifiedand adopted for transactions such as CCS aswell. In the following section we describe thesolution proposed by EBA in [3] to this prob-lem and elaborate on the possibility to exploitalternative solutions.
8In this case study we applied the procedure, described in "Quantitative approach" section, proposed by EBA and relyingon market sensitivities.
34www.iasonltd.com
Argo Magazine
Netting setTrade Nature Maturity Ccy Notional (in
USD)Pay Leg Receive Leg Market value
(in EUR)1 CCS 08/03/27 EUR/USD 300,000,000 FLOAT FLOAT 40,193,5662 Swap 08/03/47 USD 300,000,000 FIX FLOAT 19,930,0753 CCS 08/03/47 EUR/USD 300,000,000 FIX FIX 22,985,6054 Swap 08/03/47 EUR 276,192,230 FLOAT FIX -15,624,3455 CCS 19/02/19 EUR/USD 200,000,000 FLOAT FIX 16,111
Specifications of margin agreementMargin frequency MonthlyThreshold NullMinimim Transfer Amount 5,000,000Indipendent Amount NullNet collateral currently held by the bank -68,810,000
Foreign exchange risk Interest rate riskIf all the CCSs are in FX class If quantitative analysis assigned the trade n. 5 in IR class*
Alpha 1.40 Alpha 1.40Replacement Cost 136,311,011 Replacement Cost 136,311,011Multiplier 1.00 Multiplier 1.00AddOnaggr 11,708,366 AddOnaggr 30,346,977PFE 11,708,366 PFE 30,346,977EAD 207,227,128 EAD 233,321,183*In this case, we proposed to use the currency of the receive leg as hedging set currency
TABLE 4: Cross currency swap: an example of derivative transactions with ambiguous primary risk driver
Quantitative approach
When the qualitative approach fails, thesensitivities and underlying volatility must betaken into account in order to identify the pri-mary risk driver and map each transaction toone or more risk categories. In order to performthat, EBA indicates 3 steps:
• Qualitative identification of all the riskdrivers of the transaction,
• Assessment of the materiality of each riskdriver of the transaction through the com-parison of all sensitivities and volatility,
• Identification of the most material amongthese material risk drivers.
Concerning the second point, EBA proposedfour options:
1. Defining a threshold above which ‘anyrisk driver whose associated sensitivity ishigher than X% of the sensitivity of themain risk driver is deemed material’. Inthis case we have not a cap concerning thenumerosity of material risk drivers.
2. A multistep approach:
• first, calculate all the sensitivities sifor (i = 1, · · · , N) of an instrumentand set SN = ÂN
i |si|,
• then, rank them in termsof relative relevance obtaininga sequence ai where a1 =max(|s1|, · · · , |si|, · · · , |sN |),
• finally, calculate the ratio a1SN
: if itis greater than Y% the primary riskdriver is found, otherwise computethe ratio (a1+a2)
SNand we compare
with Y%, and so on in order to deter-mine one or more risk categories towhich assign the transaction.
Also in this option, we have not a cap con-cerning the numerosity of material riskdrivers but it depends on the calibrationof Y.
3. Including volatility into I or II, e.g. weight-ing sensitivities by FRTB-SBA RWs.
4. Using the SA-CCR PFE and assess the ma-teriality of sensitivities to a risk class rela-tively, by comparing PFEs with the highestPFE; or assess the materiality by consider-ing the coverage of total PFE.
Fallback approachWhen the quantitative approach fails or can-
not be implemented, the presumption is that allidentified risk factors would be deemed mate-rial. Therefore the transaction is allocated to allrisk categories to which its risk factors belong.
Conclusion
In 2014, the Basel Committee introduced amore risk-sensitive approach for CCR namedStandardised Approach for Counterparty CreditRisk (SA-CCR). In 2017, the European Banking
Issue n. 13 / 201835
Trading Book
Authority presented a discussion paper regard-ing the potential implementation issues of it. Inparticular EBA highlights two points.The first point concerns the correction of super-visory delta in context of negative rates: EBAproposed a shift parameter in order to move theinterest rate into positive area.The second point of the discussion paper re-gards the mapping of derivative transactionsto risk categories: EBA proposed a three-stepapproach based on primary risk driver andsensitivities for complex products. About thistopic, we analyzed an hybrid derivative like across currency swap, that could be assigned toFX class or IR class, and the relative impact onEAD.
The assessment based on market sensitivities(i.e. greeks) could introduce a change in theEAD from day to day with “artificial” impacton the EAD. For this reason, we are currentlyanalyzing an alternative methodology, that canbe found useful for more sophisticated banks,based on Global Sensitivity Analysis [1]. Theidea is to compute the so called Sobol’ sensi-tivity indices, instead of market sensitivities, inorder to have a more stable and precise estima-tion of the risk associated to these transactions.We plan to present the details of this methodol-ogy, as well as some concrete applications, in aforthcoming paper.
36www.iasonltd.com
Argo Magazine
References
[1] Basel Committee on BankingSupervision. The standardisedapproach for measuring counterpartycredit risk exposures. 2014. Availableonline at: http://www.bis.org.
[2] Basel Committee on BankingSupervision. Frequently askedquestions on the Basel III standardisedapproach for measuring counterpartycredit risk exposures. 2018. Availableonline at: http://www.bis.org.
[3] European Banking Authority.Discussion Paper - Implementation inthe European Union of the revisedmarket risk and counterparty creditrisk frameworks. 2017. Availableonline at:https://www.eba.europa.eu/.
[4] European Commission. Legislativeproposal 2016/0360 to amend theCapital Requirements Regulation(Regulation (EU) N. 575/2013). 2016.Available online at:https://ec.europa.eu/.
[5] Iason Consulting ltd. Comments toEBA RTS proposals on FRTB andSA-CCR. 2018. Available online at:https://goo.gl/jP3A6f.
www.iasonltd.com37
StressTest
Modelling Banking Commissions:Application to the Italian Banking System
Argo Magazine
About the Authors
Antonio Castagna:Partner and CEO of Iason Consulting ltd.Antonio Castagna is currently partner andco-founder of the consulting company IasonConsulting ltd. He previously was in BancaIMI, Milan, from the 1999 to 2006: there, hefirst worked as a market maker of cap/floor’sand swaptions; then he set up the FX optionsdesk and ran the book of plain vanilla andexotic options on the major currencies, be-ing also responsible for the entire FX volatil-ity trading. He started his carrier in the in-vestment 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, collateral man-agement, managing of exotic options risksand volatility smiles. He is also author of thebooks “FX options and smile risk” and “Mea-suring and Managing Liquidity Risk”, bothpublished by Wiley.
Email: [email protected]: https://goo.gl/NoZTsp
Federico Mondonico:Statistical Analyst.As Statistician, he develops and implementsstatistical, econometric and machine learningmethodologies in the banking and financialsector. In particular, he currently deals withthe modelling of topics related to credit risk,both from a statistical and economic-financialpoint of view.He worked at the writing of this researchduring his stint as a consultant in Iason.
Email: [email protected]: http://goo.gl/jLvbYz
www.iasonltd.com39
Stress Test
Modelling BankingCommissions:
An Application to the ItalianBanking System
aaaa
Antonio Castagna Federico Mondonico
T his paper presents a procedure for the modelling of net bank commissions (Non Interest Rate Income)as a function of macroeconomic variables. The methodology used to estimate the models is based ona Bayesian approach (BACE) method which provides the degree of relevance for each macroeconomic
variable, determining its impact in explaining the evolution of the commissions. Uses of the proceduredescribed above range from internal management purposes to regulatory and supervisory stress testing. Aquantitative analysis of the commissions is presented for the Italian banking system, at an aggregate level, andfor a sample of Italian banks, at single entity level.
An important source of revenues for thebanks is the amount of fees and com-missions they charge for the services
offered. Under this denomination fall a wide va-riety of revenues, including: commissions andfees earned from service charges, brokerage fees,origination and servicing fee income from theservicing of mortgage loans, credit card receiv-ables and other consumer and commercial loans,trust fees, management and investment bankingfees and commissions earned from real estatemanagement services (e.g.: fees for property ac-quisition and development, advisory fees, assetmanagement fees, facilities management feesand related real estate services).
In order to understand the relevance of com-missions in the banking industry, for 2015 asan example, one may consider that net commis-sion income as a percentage of Italian banks’revenues was 36.5%, one of the highest in Eu-rope as reported in the analysis by the UfficioStudi CGIA [9]. In more detail, this study showsthat in the period 2008 - 2015 the increase inthe cost of current accounts, credit cards andother banking services in Italy rose by 20%. Inthe same period in the United Kingdom the in-crease stopped at 11.5%, in France at 11.1%, in
Spain at 6.5%, while in Germany (-4.6%), Bel-gium (-7%) and especially in the Netherlands(-27%) there was a strong decrease.
Figure 7 shows the evolution of other net in-come (approximation of net commissions at anaggregate Italian level), expressed as a percent-age of intermediation margin. The percentagein recent years has been around 40%, whichonce again means the importance of net com-missions in a bank financial statement. In oneof the few empirical studies, as Mirza et al. statein [7], bank commissions represent on averagebetween 20% and 30% of the total income ofEuro-area banks and about two-thirds of banks’total non-interest income, thus confirming thefigures above.
Given these figures, it is surprising that littleattention has been paid at the modelling andanalysis of this P&L item: a list of the mostrecent works includes Coffinet et al. [2], whichinvestigates the sensitivity to adverse macroeco-nomic scenarios of the main sources of bankingincome, such as commissions, within the Frenchbanking system; ECB Financial Stability Review2013 [5], where it is pointed out that a moresystematic modelling of fees in relation to theunderlying macro-financial factors could help
40www.iasonltd.com
Argo Magazine
FIGURE 7: Percentage weight of other net income with respect to intermediation margin(Source: Banca d’Italia).
in forward-looking exercises like as stresstests, in contrast to the frequently applied as-sumption of a constant evolution and finallyKok et al. [6], in which the challenges of increas-ing commission income are discussed and someof the potential financial stability implicationsrelated to a greater reliance on these incomesources are highlighted.
The modelling of bank fees is a scarcely ad-dressed issue within banks and it is mainly con-sidered in the the stress test exercises (e.g.: EU-wide EBA stress tests), which European banksmust regularly run since 2012.
This income component was often consid-ered to be stable, but this hypothesis is too sim-plistic and does not take into account the factthat the commissions have some cyclical fea-tures. As such, treating this item independentlyof macroeconomic developments in conductingsupervisory and prudential stress tests couldlead to an underestimation of banks’ sensitivityof income in the macroeconomic shocks.
The aim of this work is to model bank com-missions so that banks can have a tool to pre-dict the trend of fees and commissions in fu-ture years, taking into account various possi-ble macroeconomic scenarios, for internal bank-ing management purposes, for ICAAP (Inter-nal Capital Adequacy Assessment Process) andstress test purposes within the ECB - EBA regu-lation.
To this end, we propose an econometricframework for estimating the relationships be-tween some macroeconomic and financial fac-tors and net banking fees using an estima-tion methodology based on a Bayesian ap-proach. More specifically, Section 2 describesthe methodology used for the modelling of the
bank charges under study, with the descrip-tion of the calibration of the models, the esti-mation and forecast of the target variable underdifferent macroeconomic scenarios. The dataused in the analyses are presented in Section 3,while the main empirical results obtained arepresented in Section 4. Finally, Section 5 showsthe conclusions reached thanks to the implemen-tation of the methodology used on commissionsin the Italian banking system.
Methodology
We will apply an econometric technique tomodelling fees and commissions; namely wewill implement a BACE approach in order toobtain the list of explanatory variables orderedby probability of inclusion in the final modeland the coefficients associated with them. Wewill outline the framework and briefly reviewthe BACE approach.
The BACE ApproachThe target variable is modelled by linear re-
gressions; in these models the behavior of a tar-get variable (net commissions) is approximatedby the linear combination of a set of indepen-dent variables (macroeconomic variables). Ba-sically, we will come up with a satellite modelbuilt in the same spirit as satellite models usedfor credit and market variables. We will use aBACE approach to identify the final model.
The Bayesian Averaging of Classical Esti-mates (BACE) is an approach for averaging lin-ear regression among a sample of possible mod-els. Its main object is to capture the goodness of
Issue n. 13 / 201841
Stress Test
fit for each model tested and then to compute,through a metric, the goodness of each inde-pendent variable included in those models. TheBACE was introduced by Sala-i-Martin et al. [8]to answer at the following question: which pre-dictors among a large sample of variables arethe best choices for the target variable? There-fore, they develop a methodology that takesinto account the goodness of fit for each model,called posterior probability, and then they used itfor disentangle, among the large set of possiblemodels given by the combination of all regres-sors, the best models from the worst ones. TheBACE is often adopted to build satellite mod-els, and more recently also for behavioural riskmodelling, as in Castagna and Scaravaggi [1].
Let us start with the definition of the generalmodel for the fees and commissions, which canbe represented as follows:
Yt =a + b1x1,t + b2x2,t + ... + brxr,t+
+ g1x1,t�1 + ... + grxr,t�1 + et(7)
where:• a: model intercept
• bi: coefficient relative to the i-th regressorat time t
• gi: coefficient relative to the i-th regressorat time t � 1
• xi,t: i-th regressor of the model evaluatedat time t
• et: error term at time t
A specific model is generated for each combi-nation of explanatory variables, after choosingthe maximum number of regressors to be in-serted in the linear regression. According to theBACE methodology, the set of possible modelsis defined taking into account all combinationsof the p independent variables, as follows:
M =K
Âk=1
p!k!(p � k)!
(8)
where M is the total number of combination, kis the model size and K is the maximum modelsize. Model size k is meant the number of inde-pendent variables included in the OLS regres-sion which belongs in the interval [1; K] with K p. In the case K = p, the number of models Mis equal to the entire set of possible combination2K.
Once the model size and the total numberof independent variables have been chosen, the
prior probability for the j-th model becomes P(Mj)= K/p.
The posterior probability is a function of themodel’s goodness of fit:
P(Mj|y) =P(Mj)T�kj/2RSS
�Tj/2j
ÂMi=1 P(Mi)T�ki/2RSS�Ti/2
i
(9)
where Mj identifies the j-th model with j, i 2[1; M], y is the observation vector on depen-dent variable, P(Mj) is the prior probability ofthe model j-th, Tj is the observation set used inestimating j-th model, kj is the number of inde-pendent variables and finally the RRSj identifiesthe Residual Sum of Squares of the j-th model.
The Bayesian averaging approach involvesthe calculation of the posterior coefficient of eachexplanatory variable entered in the OLS mod-els: it is obtained by summing the posteriorprobability of the model set M in which the ex-planatory variable is present. So we have thefollowing:
E(b j|y) =M
Âi=1
P(Mj|y)b̂i,j (10)
where b̂i,j is the coefficient of the i-th OLS esti-mate of the j-th coefficient, with j 2 JM whereJM is the set of models in which the j-th coeffi-cient is present.
In addition, the BACE provides for the cal-culation of the posterior inclusion probability (PIP)that can be referred to each explanatory variable,expressing the probability that the j-th explana-tory variable will become part of the final modelconditioned by the information obtained duringthe estimation.
P(b j|y) =M
Âi=1
P(Mi|y)H,
with H =
(1 if b j 2 Mi
0 if b j /2 Mi
(11)
This method allows to obtain probabilities thatare proportional to the level of goodness of thesingle models. In fact, equation (9) shows thatposterior probability is inversely proportionalto the residual sum of squares.
Model SpecificationIn the analyses carried out in what follows,
we identify 10 macroeconomic variables, eachtaken also at first lag, for a total of 20 regressors.
42www.iasonltd.com
Argo Magazine
This means that p corresponds to 20. Besides,we limit the number of regressors entering eachspecific model at K = 7.
Models characterized by the presence of arelevant correlation between regressors havebeen eliminated to avoid problems of multi-collinearity, just as regressions containing thesame variables at different times have been ex-cluded for practical, methodological and com-putational reasons.
The coefficients of each model are estimatedusing the method OLS and in order to correctany residual autocorrelation, the process wasgiven the possibility to include the lagged targetvariable among the regressors if specific statis-tical tests highlight the problem (e.g. Durbin-Watson test).
It should be pointed out that the BACE ap-proach is based on the fundamental assumptionthat one cannot know with certainty what thecorrect specification of the model is: one cansimply estimate each model generated by thecombinations of a given set of explanatory vari-ables and assign to each regression a weightthat determines its predictive performance.
Finally, it should be noted that, before ap-plying the BACE methodology, economic con-straints were imposed on regression coefficientsin order to consider only the economically sig-nificant contribution of the variables in the pro-cedure.
Final model and ForecastingOnce the BACE methodology has been im-
plemented, we obtain the order of relevanceof the explanatory variables, thanks to the PIP,and the estimation of the associated coefficients.The final model will contain all the explanatoryvariables, with a coefficient equal to the sum ofall coefficients associated to each explanatoryvariable appearing in the single possible models.Finally, statistics are calculated for the modelobtained in order to assess its statistical good-ness (e.g. R2, statistics related to different typesof statistical tests, etc.).
At this point, it is possible to estimate thevalues of the target variable, or the net commis-sions and fees. As described above, one of themain uses of the approach we outlined, is the
projections of this banks’ P&L item in futurescenarios. So, as an example, we will apply itto the scenarios defined by the ECB for the EU-wide stress test exercise run by EBA in 2016 [4].In more detail, two types of economic scenarioswere provided:
• Baseline scenario in which a situation char-acterized by economic stability is assumed
• Adverse scenario in which the state of theeconomy is expected to deteriorate signifi-cantly
We refer to the EBA and ECB documents for thevalues of the economic and financial variablesin each of the two scenarios.
In this way, we can assess the impact of theeconomic and financial variables on the net com-missions, especially in a situation of worseningof the economic environment.
Applications of the Framework
We present a practical application of theframework sketched above to the Italian bank-ing sector. First we present the results obtainedfrom the application of the approach on aggre-gated data for the entire banking industry, thenwe will produce a specific application to a repre-sentative sample of 6 Italian banks: Intesa San-paolo, Unicredit, UBI Banca, Banca Monte deiPaschi di Siena, Credito Emiliano - CREDEMand Banca Popolare di Milano.
Fees and CommissionsThe variable to be modelled represents the
amount of net fees in the balance sheet. Inthe application for the single banks, we usedthe data referrring to net commissions in theBankscope database for each bank; for the aggre-gated analysis, we used the data of Italian bank-ing industry available by the Banca d’Italia sta-tistical data base. The period examined rangesfrom 2005 to 2015 for the sample of banks, whileit starts in 2001 and ends in 2014 for the en-tire Italian banking system. Since the data arederived from banks’ balance sheets, they areobserved on an annual frequency.
Issue n. 13 / 201843
Stress Test
FIGURE 8: Historical series of "other net income" values from 2001 to 2014 - values in millions of euros.
Figure 8 shows the values taken from theaggregated data of Italian banks made availableby the Banca d’Italia: it can be noted that a peakwas reached before the great financial crisis in2008.
Macroeconomic and Financial Vari-ables
The independent variables (regressors or ex-planatory variables) used to model the targetvariable consist of macroeconomic variables re-lated to the Italian economy. We use severalsources: European Central Bank (ECB), Bancad’Italia and ISTAT (Italian national institute ofstatistics).
The macroeconomic variables used in theanalysis are as follows:
• Percentage change in gross domestic product(GDP)
• Inflation rate (CPI)
• Unemployment rate
• Percentage change in disposable income
• Percentage change in house price index (HPI)
• Long-term rate (10 years)
• Variation in long-term rate
• Short term rate (Euribor 3m)
• Percentage change in stock exchange index(FTSE)
• Variation in euro/dollar exchange
This set of regressors has been selected tak-ing into account the most relevant nationalmacroeconomic variables. These explanatoryvariables are included in the model at the sametime of the target variable and with reference tothe previous year.
In more detail, the coefficients relating toGDP, interest rates, inflation rate, disposable in-come, house price index and FTSE were boundto be positive, while the coefficient associatedwith the unemployment rate was imposed neg-atively. Furthermore, the regression coeffi-cient linked to the euro/dollar exchange leftunconstrained.
The selected variables provide an insightinto both the state of the financial markets andthe situation and performance of the economyin general.
Aggregated Banking System
Figure 8 shows the evolution of the histori-cal series of the net fees and commissions. Wecan see the expansionary phase before the be-ginning of the great financial economic crisis,and the downturn that occurred in 2011 duringthe strong pressure that the Italian economicsystem went under in that period.
For the aggregated analysis we identified1166 models and we estimated their coefficients.Then the BACE method has been applied, asdescribed in section 1, and the contribution ofthe explanatory variable is obtained.
44www.iasonltd.com
Argo Magazine
PosteriorDescription Coefficient Probability p-ValueConstant 29.399 1.0000 0.0000FTSE MIB Index, Percentage change, Lag 0 12.045 0.9782 0.0071Euro/Dollar Exchange, Absolute variation, Lag 1 2.883 0.6998 0.3402Euribor 3M, Level, Lag 0 2.348 0.6967 0.0004GDP, Percentage change, Lag 0 66.288 0.5763 0.0958Disposable Income, Percentage change, Lag 1 3.472 0.3882 0.2900Short Term Rate, Level, Lag 1 0.852 0.2845 0.0003HPI, Percentage change, Lag 0 1.934 0.1423 0.0595HPI, Percentage change, Lag 1 0.898 0.1237 0.0875Long Term Rate, Absolute variation, Lag 0 0.057 0.0976 0.0360Euro/Dollar Exchange, Absolute variation, Lag 0 0.110 0.0599 0.0374Disposable Income, Percentage change, Lag 0 0.210 0.0332 0.0285Unemployment Rate, Level, Lag 0 -0.019 0.0136 0.0006FTSE MIB Index, Percentage change, Lag 1 0.136 0.0131 0.0017Unemployment Rate, Level, Lag 1 -0.003 0.0032 0.0005CPI, Percentage change, Lag 1 0.118 0.0015 0.0009GDP, Percentage change, Lag 1 0.043 0.0012 0.0008
TABLE 5: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown) - original data in billions of euros.
Description Stats ResultsR2 84%P-value test Ljung-Box 73% PassedP-value test Shapiro-Wilk 91% PassedP-value test Shapiro-Francia 80% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 6: Model statistics.
Table 5 shows the list of macroeconomic vari-ables entering the final model with their asso-ciated coefficients and their posterior inclusionprobability. The table shows that the macroe-conomic variable most commonly found in themodels (with a posterior inclusion probabilityof almost 98%) and with greater explanatorypower is the percentage change in the FTSEMIB stock market index; this can be economi-cally sensible, since it indicates a general vibrantactivity in the financial markets that may gener-ate fees for banks, and also a positive economicenvironment.
The second and third most important vari-ables are, respectively: the absolute variation ofthe euro/dollar exchange rate with a lag of oneyear, even if the p-value associated with it indi-cates the low significance of the variable; andthe short-term rate represented by the 3-monthEuribor rate.
Table 6 shows the main statistics for the finalmodel. As can be seen, the R2 index provides in-formation on the goodness of the model; it is rel-atively high, confirming the good performanceof the model estimated. In addition, differentstatistics on residuals are shown, in particularp-values of different tests: the Ljung-Box testthat tests the autocorrelation of residuals (specif-
ically, the absence of correlation is accepted), theShapiro-Wilk and Shapiro-Francia tests usefulin testing the hypothesis of normality of residu-als (in this case the residuals can be considerednormally distributed). Furthermore, the t-test isused to check that the residuals have an averagezero and this test is also passed.
Furthermore, for sake of completeness, Fig-ure 9 shows the histogram of the residualswhere it is possible to see the comparison withthe normal distribution and the autocorrelo-gram. The first helps to graphically test thedistribution of residuals, while the second is aparticular graph that allows to verify the pres-ence of autocorrelation of residuals, which canbe considered absent because the bars are allcontained within the confidence interval shown.
All the statistics described above show thatthe final model is very satisfactory for mod-elling.
Let us now focus on the projections of thefees and commissions in the two different sce-narios provided in the 2016 stress tests. Theresults are in a graph (Figure 10), where thedifferent future paths followed by the fees andcommissions are shown, based on the macroe-conomic scenario.
Issue n. 13 / 201845
Stress Test
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 9: Residual analysis charts.
FIGURE 10: Forecasts under the Baseline and Adverse scenarios for 2016-2018. Values in millions of euros.
One can observe how the fees and commis-sions suffer a drop in the worst case scenario.This is due to the fact that a worsening of theeconomic performance will produce a reductionof the other net income. On the other hand, itis possible to observe that when the economicperformance is stable or improves, also the evo-lution of the fees and commissions is stable orgrows.
Table 7 shows the values assumed by thefees and commissions (or, other net income) inthe two macroeconomic scenarios and the re-spective multipliers calculated as a ratio of theprojected values to the level at the referencedate (i.e.: end of 2015), thus highlighting theexpected percentage change with respect to thestarting value.
A similar analysis has been carried out byMirza et al. [7], who consider the ratios betweennet commissions and total assets for a sampleof banks in each euro area country. We havehere used a different methodology, particularly
for the selection of variables and the estimationof coefficients. Similarly to us, they also usethe scenarios provided by the EBA for the 2016stress tests to forecast the fees and commissions.As far as the forecasts are concerned, under theadverse scenario, we find similar percentagevariations in the three years, with respect to ourstarting date. Mirza et al. [7] note that in thefirst year of the scenario most European banksare expected to decline by up to 5%, and thistrend is also fully confirmed by our model. Forthe second year they predict an increase in thenumber of countries where banks are affectedby a reduction in fees, with an average decreaseof around 5%; our forecast is also in line, whichstands at around 3.4%. The fees and commis-sions improve in the last year of the scenario,where countries with significant contractionsare reduced; the improvement is also capturedby our model, where the other net income basi-cally revert to the starting value.
46www.iasonltd.com
Argo Magazine
Year Baseline Adverse Multiplier BL Multiplier ADV2016 29880.10 28540.22 0.98 0.942017 31472.58 29354.31 1.03 0.962018 31690.30 30638.21 1.04 1.00
TABLE 7: Other net income (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Intesa Sanpaolo. (b) Unicredit.
(c) UBI Banca. (d) Monte dei Paschi di Siena.
(e) CREDEM. (f) Banca Popolare di Milano.
FIGURE 11: Forecasts under the Baseline and Adverse scenarios for 2016-2018 for the sample of 6 Italian Banks. Values inmillions of euros.
However, it should be kept in mind that theirtarget variable is not exactly the same as ours,since the commissions are related to total assets.
Sample of BanksThe sample of banks we chose can be con-
sidered representative of the Italian bankingsystem due to their importance and presencecountry-wise; we also considered the availabil-ity and robustness of the public data available.The methodology applied is the same as above:the target variable is the amount of net feesreported on the balance sheet and availablethrough the Bankscope database.
Figure 11 shows the evolution of net com-missions of selected banks: it is possible to ob-
serve the model performance and the impactof macroeconomic scenarios on the fees andcommissions.
In Table 8 we show the full details of the re-sults for one main Italian bank: Intesa Sanpaolo(details for other banks are in the Appendix).In more detail, te table show the results ob-tained by BACE methodology for each variable:the posterior inclusion probability associatedwith the variables and the estimated coefficients,which for clarity’s sake are related to regressorsexpressed in billions of euros. The variable witha higher probability of entering the final model,which is an indication of its explanatory power,is the absolute variation in the euro/dollar ex-change rate.
Issue n. 13 / 201847
Stress Test
PosteriorDescription Coefficient Probability p-ValueConstant 5.599 1.0000 0.0002Euro/Dollar Exchange, Absolute variation, Lag 0 -4.859 0.7796 0.0805FTSE MIB Index, Percentage change, Lag 0 2.696 0.7666 0.0422GDP, Percentage change, Lag 1 13.721 0.7457 0.1446Euribor 3M, Level, Lag 0 0.125 0.3890 0.0367Disposable Income, Percentage change, Lag 0 1.540 0.2446 0.1640FTSE MIB Index, Percentage change, Lag 1 0.396 0.2210 0.0163Short Term Rate, Level, Lag 1 0.022 0.1353 0.0706Euro/Dollar Exchange, Absolute variation, Lag 1 -0.140 0.0833 0.0341HPI, Percentage change, Lag 0 0.358 0.0738 0.0474Disposable Income, Percentage change, Lag 1 0.258 0.0670 0.0452GDP, Percentage change, Lag 0 0.494 0.0557 0.0347HPI, Percentage change, Lag 1 0.128 0.0409 0.0284Unemployment Rate, Level, Lag 0 -0.001 0.0310 0.0238Long Term Rate, Absolute variation, Lag 0 0.001 0.0184 0.0170
TABLE 8: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown), for Intesa SanPaolo.
Year Baseline Adverse Multiplier BL Multiplier ADV2016 6486.83 5984.70 0.98 0.912017 6646.30 6099.36 1.01 0.932018 6699.79 6364.26 1.02 0.97
TABLE 9: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios, forIntesaSanPaolo.
The relevance of the lagged variables formodelling the target variable can be explainedby the nature of the available data; in fact, thedata are extrapolated from bank balance sheetsand often affected by the influence of the pre-vious year’s economic situation, with the deter-mination of a carry-over effect.
It is interesting to note that a significant pos-itive contribution is made by gross domesticproduct, which is considered a typical indicatorof an economy’s health. Another variable thathighlights the state of the country’s economy isthe percentage change in the house price index,which is a signal of the liveliness in the origina-tion of mortgage loans. It is reasonable to thinkthat an expanding real estate sector combinedwith an expansionary phase of the economyleads to the underwriting of additional mort-gages, which generates an increase in the result-ing commissions. Finally, the negative sign asso-ciated with the unemployment rate confirms thenegative impact of general economic conditionson the fees earned by the bank.
Looking at Figure 11, the time series showsonce again a downturn caused by the un-favourable scenario of the 2016 EBA Stress Test,and a slight upward trend in the baseline sce-nario. Table 9 presents the forecasts of the com-missions in the years for the macroeconomicscenarios and their multipliers. In the Appendixwe report the details on model statistics.
Conclusion
In this article we have presented a methodol-ogy for modelling net commissions, a relevantbalance sheet item in the banking sector, by link-ing them to main macroeconomic and financialvariables. In order to do this, we have used afairly robust approach in the econometric field,the BACE technique, which is largely employedby the ECB’s in analysing and stress testing thebanking industry performance.
We have practically tested the approach inthe Italian banking industry, both at an aggre-gated system level, and at single institutionlevel, for a sample of 6 banks. The models esti-mated using the BACE methodology are verysatisfactory under a statistical point of view, de-tecting significant relationships between the feesand commissions, and macroeconomic variables.The resulting models can be used for severalpurposes, ranging from managerial planningand forecasting, to ICAAP stress tests, includ-ing scenario analysis run for regulatory reasonsas required by the European Banking Authorityand the European Central Bank on regular basisby now.
The approach seems promising and robustalso to applications to other countries.
48www.iasonltd.com
Argo Magazine
References
[1] Castagna A., Scaravaggi A. ABenchmark Framework for NonMaturing Deposits: An Application toPublic Data Available from Bancad’Italia. Argo Magazine, Winter2018. Available online at:https://goo.gl/H3MnZN.
[2] Coffinet J., Lin S., Martin C. Stresstesting French banks’ income. Banquede France Working Paper, N. 242(2009)
[3] De Bonis R., Farabullini F.,Rocchelli M., Salvio A. EconomicHistory Working Papers. Bancad’Italia, 2012.
[4] European Banking Authority. 2016EU-Wide Stress Test. EBA, 2016.
[5] European Central Bank. TheDynamics of Fee and CommissionIncome in Euro Area Banks.. FinancialStability Review, 65-67 (2013).
[6] Kok C., Mirza H., Móré C.,Pancaro C. Adapting bank businessmodels: financial stability implicationsof greater reliance on fee andcommission income. Special Feature,Financial Stability Review, ECB,2016.
[7] Mirza H., Moccero D., Pancaro C.Satellite model for top-down projectionsof banks’ fee and commission income.Stress-Test Analytics forMacroprudential Purposes in theeuro area ed. by Dees, Henr andMartin, Chapter 7, EuropeanCentral Bank, 2017
[8] Sala-i-Martin X., Doppelhofer G.,Miller R.I. Determinants ofLong-Term Growth: A BayesianAveraging of Classical Estimates(BACE) Approach. The AmericanEconomic Review, 2004.
[9] Ufficio Studi CGIA .Banche: IClienti Italiani Sono i Più Tartassati inUE. CGIA Mestre, 2016.
www.iasonltd.com49
Stress Test
Appendix
Modelling Banking Commissions:An Application to the Italian Banking System
A. Regressors and expectedcontribution
Description Expected SignPercentage change in gross domestic product (GDP) +Percentage change in gross domestic product (GDP), Lag 1 Year +Inflation rate (CPI) +Inflation rate (CPI), Lag 1 Year +Unemployment rate -Unemployment rate, Lag 1 Year -Percentage change in disposable income +Percentage change in disposable income, Lag 1 Year +Percentage change in house price index (HPI) +Percentage change in house price index (HPI), Lag 1 Year +Long-term rate (10 years) +Long-term rate (10 years), Lag 1 Year +Variation in long-term rate +Variation in long-term rate, Lag 1 Year +Short term rate (Euribor 3m) +Short term rate (Euribor 3m), Lag 1 Year +Percentage change in stock exchange index (FTSE) +Percentage change in stock exchange index (FTSE), Lag 1 Year +Short term rate (Euribor 3m) +Short term rate (Euribor 3m), Lag 1 Year +Variation in euro/dollar exchange UnconstraintVariation in euro/dollar exchange, Lag 1 Year Unconstraint
TABLE 10: List of variables used as regressors and expected sign to explain the target variable.
50www.iasonltd.com
Argo Magazine
B. Detailed level analysis
B.1 Intesa Sanpaolo
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 12: Residual analysis charts.
Description Stats ResultsR2 47%P-value test Ljung-Box 11% PassedP-value test Shapiro-Wilk 31% PassedP-value test Shapiro-Francia 45% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 11: Model statistics.
www.iasonltd.com51
Stress Test
B.2 Unicredit
PosteriorDescription Coefficient Probability p-ValueConstant 7.716 1.0000 0.0001FTSE MIB Index, Percentage change, Lag 1 0.774 0.5946 0.0612Euro/Dollar Exchange, Absolute variation, Lag 0 -0.896 0.5690 0.1245Short Term Rate, Level, Lag 1 0.164 0.5321 0.0144Euribor 3M, Level, Lag 0 0.137 0.3662 0.0045CPI, Percentage change, Lag 0 3.750 0.226 0.0329HPI, Percentage change, Lag 1 0.514 0.2182 0.1646Long Term Rate, Absolute variation, Lag 0 0.017 0.1973 0.0709Disposable Income, Percentage change, Lag 0 0.765 0.1398 0.0658Long Term Rate, Absolute variation, Lag 1 0.005 0.1332 0.0781Long Term Rate, Percentage change, Lag 0 0.010 0.1224 0.0502GDP, Percentage change, Lag 1 0.473 0.1114 0.0647CPI, Percentage change, Lag 1 0.645 0.1090 0.0568GDP, Percentage change, Lag 0 0.561 0.1061 0.0695Long Term Rate, Percentage change, Lag 1 0.005 0.1033 0.0547Unemployment Rate, Level, Lag 0 -0.013 0.0599 0.0006HPI, Percentage change, Lag 0 0.140 0.0444 0.0284Unemployment Rate, Level, Lag 1 -0.005 0.0228 0.0006Disposable Income, Percentage change, Lag 1 0.011 0.0048 0.0037
TABLE 12: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown).
Year Baseline Adverse Multiplier BL Multiplier ADV2016 7599.04 7447.50 0.99 0.982017 7474.08 7293.16 0.98 0.952018 7750.57 7523.73 1.01 0.99
TABLE 13: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 13: Residual analysis charts.
Description Stats ResultsR2 82%P-value test Ljung-Box 12% PassedP-value test Shapiro-Wilk 72% PassedP-value test Shapiro-Francia 67% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 14: Model statistics.
52www.iasonltd.com
Argo Magazine
B.3 UBI Banca
PosteriorDescription Coefficient Probability p-ValueConstant 1.112 1.0000 0.0004GDP, Percentage change, Lag 1 1.356 0.7588 0.0892FTSE MIB Index, Percentage change, Lag 0 0.311 0.7196 0.0218Euro/Dollar Exchange, Absolute variation, Lag 0 -0.688 0.7191 0.0362Euribor 3M, Level, Lag 0 0.020 0.6061 0.0513CPI, Percentage change, Lag 1 3.809 0.5295 0.0561Disposable Income, Percentage change, Lag 0 1.504 0.5225 0.0605FTSE MIB Index, Percentage change, Lag 1 0.048 0.2542 0.0058Euro/Dollar Exchange, Absolute variation, Lag 1 -0.079 0.2524 0.0149Disposable Income, Percentage change, Lag 1 0.136 0.1724 0.0455Short Term Rate, Level, Lag 1 0.001 0.0875 0.0338Long Term Rate, Absolute variation, Lag 0 0.001 0.0862 0.0367HPI, Percentage change, Lag 1 0.028 0.0710 0.0321HPI, Percentage change, Lag 0 0.027 0.0682 0.0342GDP, Percentage change, Lag 0 0.047 0.0323 0.0075
TABLE 15: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown).
Year Baseline Adverse Multiplier BL Multiplier ADV2016 1237.05 1189.90 0.97 0.932017 1258.09 1204.56 0.99 0.942018 1271.59 1229.76 1.00 0.96
TABLE 16: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 14: Residual analysis charts.
Description Stats ResultsR2 76%P-value test Ljung-Box 85% PassedP-value test Shapiro-Wilk 83% PassedP-value test Shapiro-Francia 95% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 17: Model statistics.
www.iasonltd.com53
Stress Test
B.4 Banca Monte dei Paschi di Siena
PosteriorDescription Coefficient Probability p-ValueConstant 1.320 1.0000 0.0102Euro/Dollar Exchange, Absolute variation, Lag 0 -2.044 0.9877 0.0361FTSE MIB Index, Percentage change, Lag 0 0.795 0.9778 0.0770Disposable Income, Percentage change, Lag 0 3.365 0.7414 0.0787Long Term Rate, Percentage change, Lag 0 0.073 0.6949 0.0208Unemployment Rate, Level, Lag 1 -0.009 0.5235 0.2368Short Term Rate, Level, Lag 1 0.011 0.3372 0.1514Long Term Rate, Percentage change, Lag 1 0.018 0.1575 0.0243Long Term Rate, Absolute variation, Lag 0 0.007 0.0887 0.0078CPI, Percentage change, Lag 1 0.334 0.0545 0.0215GDP, Percentage change, Lag 0 0.041 0.0469 0.0373CPI, Percentage change, Lag 0 0.236 0.0335 0.0095Euro/Dollar Exchange, Absolute variation, Lag 1 -0.001 0.0117 0.0101
TABLE 18: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown).
Year Baseline Adverse Multiplier BL Multiplier ADV2016 1743.14 1610.12 0.97 0.892017 1776.08 1652.24 0.99 0.922018 1822.52 1733.60 1.01 0.96
TABLE 19: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 15: Residual analysis charts.
Description Stats ResultsR2 71%P-value test Ljung-Box 14% PassedP-value test Shapiro-Wilk 24% PassedP-value test Shapiro-Francia 16% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 20: Model statistics.
54www.iasonltd.com
Argo Magazine
B.5 Credito Emiliano - CREDEM
PosteriorDescription Coefficient Probability p-ValueConstant 0.314 1.0000 0.0002FTSE MIB Index, Percentage change, Lag 0 3.451 1.0000 0.0009Euro/Dollar Exchange, Absolute variation, Lag 0 -5.374 1.0000 0.0039GDP, Percentage change, Lag 1 12.321 1.0000 0.0033Euribor 3M, Level, Lag 0 0.132 0.9846 0.0201Long Term Rate, Percentage change, Lag 0 0.125 0.9482 0.0069Disposable Income, Percentage change, Lag 0 0.837 0.4916 0.1056CPI, Percentage change, Lag 0 0.355 0.0303 0.0038Long Term Rate, Absolute variation, Lag 0 0.001 0.0146 0.0026Long Term Rate, Percentage change, Lag 1 0.001 0.0086 0.0019HPI, Percentage change, Lag 1 0.007 0.0051 0.0029CPI, Percentage change, Lag 1 0.052 0.0037 0.0018HPI, Percentage change, Lag 0 0.003 0.0020 0.0011Disposable Income, Percentage change, Lag 1 0.002 0.0016 0.0012
TABLE 21: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown).
Year Baseline Adverse Multiplier BL Multiplier ADV2016 426.36 406.87 0.95 0.912017 437.32 422.06 0.97 0.942018 444.81 431.89 0.99 0.96
TABLE 22: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 16: Residual analysis charts.
Description Stats ResultsR2 98%P-value test Ljung-Box 32% PassedP-value test Shapiro-Wilk 57% PassedP-value test Shapiro-Francia 36% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 23: Model statistics.
www.iasonltd.com55
Stress Test
B.6 Banca Popolare di Milano
PosteriorDescription Coefficient Probability p-ValueConstant 0.525 1.0000 0.0009FTSE MIB Index, Percentage change, Lag 0 0.144 0.9971 0.0242Euro/Dollar Exchange, Absolute variation, Lag 0 -0.227 0.9937 0.0692GDP, Percentage change, Lag 0 1.238 0.9776 0.0414Short Term Rate, Level, Lag 1 0.019 0.9733 0.0224Disposable Income, Percentage change, Lag 0 1.091 0.9686 0.0717Long Term Rate, Percentage change, Lag 0 0.001 0.2220 0.1300Long Term Rate, Absolute variation, Lag 0 0.001 0.2117 0.1110Long Term Rate, Percentage change, Lag 1 0.001 0.1502 0.1115HPI, Percentage change, Lag 1 0.007 0.0226 0.0105HPI, Percentage change, Lag 0 0.003 0.0050 0.0014
TABLE 24: Final regressors, regression coefficients, posterior inclusion probabilities and statistical significance (only finalregressors with a PIP greater than 0.0001 are shown).
Year Baseline Adverse Multiplier BL Multiplier ADV2016 581.17 546.32 0.95 0.902017 586.47 533.53 0.96 0.882018 596.06 568.99 0.98 0.93
TABLE 25: Commissions (in millions of euros) and multipliers in the Baseline (BL) and Adverse (ADV) scenarios.
(a) Histogram of residuals. (b) Autocorrelation function of resid-uals.
FIGURE 17: Residual analysis charts.
Description Stats ResultsR2 96%P-value test Ljung-Box 25% PassedP-value test Shapiro-Wilk 73% PassedP-value test Shapiro-Francia 81% PassedP-value t-test (Residual average = 0) 100% Passed
TABLE 26: Model statistics.
56www.iasonltd.com
Argo Magazine
In the previous issue
Issue N. 12 - 2018
ARGONew Frontiers in Practical Risk Management
1
aaaa
Winter 2018
Alm & Irrbb
A Benchmark Framework for NonMaturing Deposits: An Application toPublic Data Available from Banca d’Italia
Trading Book
The Effects of FRTB in the CVA RiskFramework
Last issues are available at www.iasonltd.com/research/
www.iasonltd.com57
Iason is an international firm that consults
Financial Institutions on Risk Management.
Iason is a leader in quantitative analysis and
advanced risk methodology, offering a unique
mix of know-how and expertise on the pricing
of complex financial products and the
management of financial, credit and liquidity
risks. In addition Iason provides a suite of
essential solutions to meet the fundamental
needs of Financial Institutions.
1
