Post on 10-Mar-2021
transcript
The xVA prism:
Current challenges and best
practices 6 February 2014
Alexander Antonov, SVP, Head of Quantitative Research
Alexis Hamar, Sales Manager
Agenda
1. Introduction to Numerix
2. Overview of the regulatory landscape & current market trends
3. The new margining regime: Accounting for collateral under an
unified decision measure
4. Valuation Adjustments and replication
5. Conclusions
Section I
Introduction to Numerix and Numerix Solutions overview
Numerix Overview
Market leader in Advanced analytics for structuring/managing all derivatives and structured products and risk
management and compliance
200+ employees globally
Integrated in 3rd party solutions (trading, risk and operations platforms)
Some of our clients Strong resource pool Global coverage, with support
across all major languages
Phds 40%
MBA/Msc 30%
CFA 20%
MA 10%
Section II
Overview of the regulatory landscape and current Market trends
The new regulatory framework for counterparty risk
Basel 3 Capital requirement for OTC bilateral exposures and exposures to CCPs
(from January 2014)
IFRS 13 Accounting rules for CVA/DVA – since January 2013
All standardized OTC derivatives should be cleared through CCPs
OTC derivative contracts should be reported to trade repository
Exemptions: sovereign and corporates (thresholds, hedging) – III/IVQ 2013
Mandatory Clearing for eligible OTC Derivatives – June 2014
Margin requirement for non centrally cleared OTC – from Dec 2015
EMIR
Solvency
2
Solvency incentivizes high quality collateral selection – From January
2016
BCBS/IOSCO Mandatory initial margin and variation margin for bilateral OTC transactions
Segregation and limits to rehypotecation of the amount of collateral that
covers initial margin; universal threshold established. Phase in from dec
2015
• The new regulatory requirements have accelerated the development and re-definement of valuation and risk methodologies at institutions across the globe with a focus on valuation transparency, margin assessment and risk fortification.
Regulatory-Compliance
Margining & Valuation
Model Validation
Total Value Adjusment
Data & systems
Current market trends
• « New » regime based on Initial/Variation Margin and Collateral Posting
• Funding inclusion into pricing aka funding monetization
• Collateral Choice in pricing and optionality (CTD)
• Multi-Curve Pricing
• Confidence in the appropriateness of the model (local adaptation)
• Transparency for model and parameters
• Confidence that the entity has a good understanding of
assumptions, risk drivers and results
• Stress Testing
• Understanding Pricing/Risk decomposition : CVA, DVA, FVA, RVA,…
• Risk Integration : market+credit+liquidity in a consistent unified
framework
• Term Structure of eg Multi year TVA
• Continued investment in data and systems, increasing
computation speed and embedding within front office tools and
P&L
• Reporting and data Intelligence for real time
Longdated “Unclearables”
Source: ISDA Margin Survey 2013 Source: Tabb Group
Growth in value of collateral agreements for non-cleared OTC derivatives Notional amount outstanding has grown over the last decade. Aggregate counterparty exposure in terms of net
MtM value considering close out netting before collateral has decreased from 3,9 to 3,7 billions Usd from 2011
to 2012 (BIS statistics); collateral value reported has increased, suggesting more exposures being
collateralized.
Collateral Transformation & Trends
• Mostly handled in the back office
• Low necessity of margin calls (high thresholds and min transfer
• amounts
• Few derivatives were collateralized
Before 2008
• Lack of transparency in Structured Credit Notes
• Double Defaults tendency
• One rate regime
• Regulatory Haircuts
2008- 2012 • Increased usage of collateral as a way
to mitigate risk of counterparty default
• Regulation requirements – CCPs – Margin calls
• Divergence of rates after the crisis and complex CSAs
• Collateral shortage (high demand, rehypothecation)
• Equally important for sell-side and buy-side
• Choice of collateral significantly affects derivative pricing
• Push from traders and front-office – profit is the drive
Now
Section III
The new margining regime: Accounting for collateral under an unified
decision measure
Initial & Variation Margins
• The initial margin is supposed to cover quality of collateral, gap
risk, wrong way risk. By design the IM needs to cover the closing
out of positions (without the loss) to a CCP in a worst case
scenario.
• Initial margin is an “haircut” (overcollaterisation) which is
calculated at inception of the trade. The margin can fluctuate
during the liftetime of the trade, given market conditions and
remaining risk.
• As its colour varies, several methodologies exist, two of them are
proposed for cleared and uncleared positions.
– Cleared position :It is calculated as an historical VaR
capturing a cycle (5-10 years) observation, on shifts of
underlying market factors.
– Uncleared position : It is calculated as a Potential Future
Exposure (99% quantile) at 10 day horizon over a stressed
market period.
• The Variation margin covers the change in the valuation of the
relevant positions as with the collateral in a standard CSA.
• There is a notion of risk transformation of counterparty risk into
liquidity/funding risk, operational and legal risks.
Pricing & Ageing
Hybrid Model
Historical VaR (cleared) or PFE (uncleared)
Haircut Optionality
MTA Thresholds
Collateral
Data
Initial Margin
Variation Margin
FVA
CVA , DVA , RVA, CollVA
Collateral
Data
Counterparty Risk Platform
CSA-Netting agreements/
Path dependent Collateralized
Historical
VaR 10 day PFE
Risk Mitigation Strategies
IR
(S)BK2F
EQ
Heston
FX
Heston
IR
HW1F
IR
(S)BK1F
IR
HW2F
IR
SV-LMM
INF JY
(HW)
INF JY
(BK)
EQ
BS
EQ
Dupire
EQ
Bates
EQ
LSV
FX
BS
CMDTY
Black
CDMTY
S1F
CMDTY
GS2F
CMDTY
Heston
HYBRID
MODEL
-100.00
-50.00
-
50.00
100.00
150.00
200.00
250.00
300.00
4/1/2012 8/14/2013 12/27/2014 5/10/2016 9/22/2017 2/4/2019 6/18/2020
PFE w Collateral
PFE w/o Collateral
Overall Framework
EVA / Limits
PnL
Variations
Stress Testing Models
13
Credit Value
Adjustment
Debit Value
Adjustment
Replacement
Value Adjustment
Margining Value
Adjustment
Funding Value
Adjustment
Risk Cocktail :Valuation Adjustments
Collateral Value
Adjustment
The cocktails ingredients
• The final commercial margin include the following ingredients:
• CVA (Credit Value Adjustment) :Adjustment to the risk free value made by one agent to take into account the potential default of a counterparty defaulting first.
• DVA (Debit Value Adjustment): Adjustment to the risk free value made by the agent to take into account the his potential default first than the counterparty. It also incorporates a funding angle, as bank’s default risk increases, the value of liabilities decreases.
• FVA (Funding Value Adjustment)/LVA: Reflects the cost an institution incurs when hedging an uncollateralized trade with an offsetting position on which collateral is required.
• RVA (Replacement Value Adjustment): reflects the “trigger” cost that replaces a credit quality downgrade of the counterparty with another trade from another counterparty.
• MVA (Margin Value Adjustment): reflects the cost associated with Initial and Variation Margins
• Cost of Capital : Valuation Adjustment for Regulatory Capital
• CollVA: Cost of collateral (embedded options, currencies,..)
CVA Example: Numerix - Datawatch
CVA Example: Numerix - Datawatch
Section IV
Valuation Adjustments and Replication
Origins of xVA
• In the modern world:
– existence of multiple rates corresponding to different possibilities to borrow/lend
money
• rate rx collateral rate (almost risk-free rate)
• rate rr for asset secured borrowing (“repo”)
• rate rf for unsecured funding
• Possibility of default and migration
the classical arbitrage-free theory should be modified
• We should modify the replication/hedge arguments to include multiple rates and
defaults
• Definition. The TVA (Total Valuation Adjustment) is the difference between the true
(modern) price and the base one. The base price is often related with fully
collateralized portfolio.
Financial instrument replication (hedging) is a unique way to calculate its fair
price or adjustments xVA (CVA, DVA, FVA etc.)
Different replications lead to different adjustments. There is a big variety of the
adjustments (CVA, DVA, FVA, FCA etc.). Thus, it is important to identify them for
given replication techniques to avoid double-counting.
A portfolio replication (bonds) strategy is designed and used in the context of
hedging default risks for both self and counterparty.
Hedge (replication) against different market movements and defaults: Credit spread and default of the counterparty and the bank
Funding costs of the counterparty and the bank
Assets movements
Collateral rate movements
Introduction and market movements
Piterbarg (2010)
Borrow/lend money via the bank treasury desk with a unique “funding” rate
The bank default is already taken into account by the treasury "integrated"
rate
Burgard-Kjaer (2013)
Borrow/lend money with external (w.r.t. the bank) parties: different rates to
borrow and lend.
The rates are related with the bank credit spread and expected recovery.
Multiple replication strategies
Replications/Hedging
Double-counting counterbalancing effects
Banks are required to hold a DVA adjustment for their own credit risk on
uncollateralized trades
Funding spreads are a function of bank credit quality: by implementing FVA you
are effectively subsuming DVA on payables and accounting for funding on
receivables
Knowledge of the replication/hedging strategy: gives the unique pricing equation and specifies the TVA
permits to identify parts of the adjustments with xVA’s
prevents from the double-counting • if we calculate the FVA coming from Piterbarg replication, it will be double-counting to take the
DVA into account;
• if we follow Burgard-Kjaer perfect replication using two bonds, the TVA=CVA+DVA, i.e. using
Piterbarg FVA instead of the DVA will lead to errors
Implementation
1. Simulate the model rates and all payment indexes
2. Build the single-rate pricing model equipped with Least Square Monte Carlo
3. Calculate future values for all instruments in portfolio on this model (can be
done independently ”instrument-by-instrument” using the Algorithmic Exposure
methods (AIM (2011))– important for parallel computation)
4. Aggregate the instrument future prices into the portfolio ones
5. Calculate the xVA from the obtained future values using universal approximation
formula (ABM (2013)) and its scripted version available in Numerix 1. Alexandre Antonov; Numerix FVA for General Instruments: Theory and Practice
Script example
1. Alexandre Antonov; Numerix FVA for General Instruments: Theory and Practice
PRODUCTS
NONDISCOUNTING SpreadIntegral, FVA
NONDISCOUNTING CollateralUnits
TEMPORARY dt, RHS, EffectiveRate, EffectiveSpread, Delta
TEMPORARY Collateral, Collateral0, V0, RHS0
END PRODUCTS
PAYOFFSCRIPT
IF ISACTIVE(MarginCallDates) THEN
Collateral = CollateralUnits * CollateralAssetValue
Delta = MAX(V - HighT, 0) - MAX(- V - LowT, 0) - Collateral
Delta = WHEN((Delta > 0) AND(Delta < CTPYMTA), 0, Delta)
Delta = WHEN((Delta < 0) AND(Delta > - SELFMTA), 0, Delta)
Collateral += Delta
CollateralUnits = Collateral / CollateralAssetValue
END IF
IF ISACTIVE(ObservationDates) THEN
// Calculate true collateral amount
Collateral = CollateralUnits * CollateralAssetValue
// Calculate the true RHS (based on true collateral amount)
RHS = Collateral * r_C + (V - Collateral) * r_F
// Regularization procedure for effective rate calculation:
// Calculate regularized price floored/capped to +-Tolerance
// when V close to zero
V0=WHEN(V>=0, MAX(V, Tolerance), MIN(V, - Tolerance))
// Calculate regularized collateral (ignoring margin call dates and MTA)
// and corresponding regularized RHS
Collateral0 = MAX(V0 - HighT, 0) - MAX(- V0 - LowT, 0)
RHS0 = Collateral0 * r_C + (V0 - Collateral0) * r_F
// Calculate regularized effective rate protected from division by zero
// The approximation error is small (higher order than our accuracy)
EffectiveRate = RHS0 / V0
EffectiveSpread = EffectiveRate - r_M
dt = ObservationDatesDCF
SpreadIntegral += EffectiveSpread * dt
// Aggregate the FVA
FVA -=(RHS - r_M * V) * exp(- SpreadIntegral) * DF * dt
END IF
END PAYOFFSCRIPT
Section IV
Conclusions
Conclusions and potential extensions
Funding and Credit are untimely, implicitly linked and their interplay causes
(some) counterbalancing effects:
The Initial Margin “wave” for both cleared and non cleared instruments imply higher capital
requirements, with higher funding necessity.
FVA & DVA monetization dynamics, where DVA, generates funding benefits in asymmetric
situations.
Systems & Technologies exist today for achieving an integrated xVA approach
to derivative front-to-treasury-risk process
Numerix provides a transparent and complete modeling framework on the xVA
including a set of script templates embedded in platforms as well as a detailed
description of replication strategies and associated adjustments (CVA, DVA,
FVA etc.)
References
Alexandre Antonov, Serguei Issakov and Serguei Mechkov (2011)
"Algorithmic Exposure and CVA for Exotic Derivatives", Available at SSRN
Alexandre Antonov, Marco Bianchetti and Ion Mihai (2013)
"FVA for General Instruments: Theory and Practice", Available at SSRN
Christoph Burgard and Mats Kjaer (2013),
"Funding strategies, funding costs", RISK, Dec
Vladimir Piterbarg (2010),
"Funding beyond discounting: collateral agreements and derivatives pricing",
RISK, Feb.