CVA, Basel III and Wrong-Way Risk

Transcription

1 CVA, Basel III and Wrong-Way Risk Dan Rosen Regulatory Capital and CVA Mark-to-market losses due to credit valuation adjustments (CVA) were not directly capitalised. Roughly two thirds of CCR losses were due to CVA losses and only onethird were due to actual defaults. Basel Committee on Banking Supervision (29)

2 Outline Introduction CCR, CVA, management of CVA CCR capital and Basel III Wrong-way risk (WWR) Computing CVA and CVA VaR Wrong-way risk methodology Examples Concluding remarks Counterparty Credit Risk Evolution Economic capital Default risk Basel II (IRB) EPE and alpha Counterparty exposures and limits Hedging CCR JtD risk and CVA CCR valuation: CVA Fundamental vs. Market values (CDS spreads) Unilateral bilateral Economic capital Credit + market risk (CVA) Basel III... CVA is now an integral part of current accounting rules for P&L, and of the new proposal for banking regulation ( Basel III rules)

3 Pricing CCR: Credit Value Adjustment (CVA) CVA is the market value of counterparty credit risk CVA = Risk-free portfolio value true portfolio value accounting for counterparty s default CVA is an integral component of the value of derivatives Now an integral part of accounting rules, and Basel III Prior to mid-27, CVA was either ignored by dealers, or too small to be noticed by customers CVA is measured at the counterparty level Ideally, it should be part of the trade valuation but calculated separately because of portfolio effects In addition to credit spreads (and competition) the CVA charged on a particular trade is affected by: Bank s existing portfolio of trades and the credit mitigation used in the deal Methodology used to determine exposures CVA and Risk Management Some banks started to price and hedge CVA in the mid 199s More recently, more banks started to price and actively hedge CVA Banks currently calculate and manage CVA according to different business models and subject different accounting regimes Various large banks already manage CVA risks as part of their Trading Books: daily MtM, active hedging, enforced market risk limits and intent to transfer out the CVA risks Some banks have opted for central CVA desk Others have opted for CVA desks deployed in their main business units CVA desks sell full counterparty credit insurance to the derivatives trading desks Manage the risks of the CVA after inception of the trades Subject to risk limits and usually do not have a revenue generation budget IACPM 3

4 Dan Rosen Some Definitions Counterparty exposure: economic loss incurred on all outstanding transactions if counterparty defaults Cost of replacing or hedging the contracts at the time of default Accounts for netting and collateral, but is generally not adjusted by possible recoveries More generally, exposures can also be defined as potential losses on credit migration events such as downgrades (e.g. in CreditMetrics) Potential future exposure (PFE): current exposure plus the potential future changes in exposures during the contracts lives Accounts for the aging of the portfolio and underlying market factor movements which directly affect contract values at a future times Example: a pay-fix IRS with negative MtM has current exposure =. If future rates rise, the contract can have a positive value potential exposure to holder Computing CVA Value of the CP portfolio at t N = i i= 1 V ( t) V ( t) Gross CP-level exposure (netting not allowed) Netted CP-level exposure (single agreement) N = i= 1 ( ) max{, V ( t) } E t { V t } E( t) = max ( ), i CP-level (margined) { } E( t) = max V ( t) C( t), 35 3 Counterparty PFE Mean Exposure 95 Percentile Cond. EPE 25 Instantaneous collateral C( t) = max V ( t) H, Lagged collateral { } { δ } C( t) max V ( t t) H, = 5 Exposure ( Million) CP portfolios with multiple netting agreements and trades outside of the Time (days) agreement can be modeled by a combination of these equations

5 Time Time Dan Rosen CCR Credit Risk Model Components Exposures Default Migration t t Recovery CCR and Potential Future Exposures (PFEs) Simulation 2. (Valuation) Pricing Instruments Assets Mark-to-Future V (p, S, t) Values Scenarios 1. Risk Factor 1.Risk Scenario factors scenarios Generation generation Counterparties 3. CP aggregation, 3. Exposure mitigation generation collateral) PFE (P, S, t) (netting, collateral...) 4. Exposures 4. PFE statistics Statistics Effective EPE (T) Effective Expected Exposure Maximum Peak Exposure (T) Peak Exposure (95%) Source: de Prisco and Rosen (25) EPE (T) Expected Exposure 5

6 Credit Losses and CVA Unilateral CP-level CVA the bank s discounted loss due to the CP default (recovers a fraction R of the exposure ) CVA obtained by discounting losses and applying the expectation where 1 T L = { } (1 R ) E ( τ ) D τ ( τ ) CVA = (1 R) dp( t) eˆ ( t) [ ] eˆ ( t) = E ˆ t D( t) E( t) E D( t) E( t) τ= t is the risk-neutral discounted expected exposure (EE) at t, conditional on the CPs default at t T (everything is under the risk-neutral measure) Calculating Exposures and CVA by Simulation Banks use Monte Carlo simulation in practice to obtain the distribution of counterparty-level exposures The calculation of CVA and CVA contributions can be easily incorporated to the Monte Carlo simulation of the counterparty-level exposure In general, exposures are simulated separately implicitly assume that they are independent of counterparties credit quality Conditional expectations in the CVA formulae can be replaced by the unconditional ones Dependence of exposure on the counterparty s credit quality can be incorporated in the CVA calculation, if the trade values and credit quality of the bank s counterparties are simulated jointly (both right/wrong-way risk and exposure-limiting agreements) E.g. using a joint process with stochastic intensities, or a copula methodology as in Garcia cespedes et al Need to make model computationally efficient

7 Dan Rosen Calculating CVA Simulation Unilateral CVA Independent market and credit risk CVA = (1 R) e ( tk )[ P( tk ) P( tk 1)] 1 M ( j) ( j) ( k ) ( ) ( ) j= 1 k k e t = D t E t M k Counterparty PFE 35 Mean Exposure 3 95 Percentile Cond. EPE 25 2 Exposure ( Million) Time (days) Analytical CVA (Normal Approx.) It is useful in practice to estimate EE, CVA V ( t) = µ ( t) + σ ( t) X i i i i an CVA contributions quickly outside of the simulation system Analytical expression s can be derived for EE and CVA contributions, for the case when trade values are normally distributes Independent market and credit: contributions without collateral [ ] eˆ ( t) = E ˆ t D( t) E( t) E D( t) E( t) τ= t µ ( t) µ ( t) e( t) = µ ( t) Φ + σ ( t) φ σ ( t) σ ( t) µ ( t) µ ( t) H e( t) = µ ( t) Φ Φ σ ( t) σ ( t) µ ( t) µ ( t) H µ ( t) H + σ ( t) φ φ + HΦ σ ( t) σ ( t) σ ( t) 7

8 CCR and CVA Capital Charges in Basel III Basel III introduces a new charge for MtM losses (CVA spread risk): associated with a deterioration in the credit worthiness (greater source of losses than outright defaults) The total CCR charges aim to cover default, migration and spread risks Total CCR capital = CCR (default) capital + CVA risk capital Revision of Internal Model Method (IMM) for measuring exposures based on Effective EPE with stressed parameters address wrong-way risk Default risk capital charge: greater of Portfolio capital charge based on Eff EPE using current market data Portfolio capital charge based on Eff EPE using stressed calibration CCR Capital Carge (Basel II) Basel Capital EAD = N j= 1 N LGD j EAD j N j = Eff EPE j α 1 1 ( PD ) ρ N (.1) α = j j 1 ρ EC EC j T ( L ) ( L ) EPE PD j MF ( M, PD ) Credit losses random exposures Credit losses deterministic exposures (EPE) j j Eff EPE = effective EPE (expected positive exposure) Alpha: measures the effect of using deterministic exposures (EPE) instead of stochastic exposures ratio of EC from a joint simulation of market and credit risk factors EC when CP exposures are constant and equal to EPE Eff EPE and M (maturity) based on bank s internal model Supervisory alpha = 1.4 allow for own estimate, subject to floor =

9 Mean Exposure 95 Percentile Cond. EPE Dan Rosen CVA Risk Capital Charge CVA capital charge calculation depends on bank s approved methods for CCR and specific interest rate risk Historical simulation, Monte Carlos simulation, etc. Full repricing, sensitivities to specific tenors, sensitivities to parallel shifts (CS1), second order sensitivities, etc. Advanced CVA capital charge Impact of changes in the counterparties credit spreads on the CVAs of all OTC derivative counterparties, together with eligible CVA hedges Using the bank s VaR model for bonds restricted to changes in credit spreads, and does not model the sensitivity of CVA to other factors CVA capital charge includes general and specific credit spread risk Includes stressed VaR but excludes IRC VaR = non-stressed VaR + stressed VaR CVA VaR: Market Risk Capital and VaR From a market risk perspective, CVA is just essentially another price risk Standard techniques to measure market VaR Full simulation Sensitivities Very expensive re-pricing Simple approximations sought Regulatory Basel III focuses only on spread risk Portfolio loss distribution Probability 1-day 99% VaR.12 Empirical.1 Normal Counterparty PFE Size of Loss (thousands USD) Exposure ( Million) CVA = (1 R) dp( t) eˆ ( t) T [ ] eˆ ( t) = E ˆ t D( t) E( t) E D( t) E( t) τ= t Time (days)

10 CVA Calculation and Basel III Formula ( 1 R) eˆ ( t ) [ P( t ) P( t )] CVAWWR = k k k k 1 Regulatory CVA formula Calibration Spreads For individual CPs where available, otherwise proxy by rating, industry, region For stressed VaR using the most severe one-year period in the exposure stressed calibration EE Non-stressed VaR EE with current parameter calibration of exposures Stressed VaR EE according to stressed exposure calibration CVA Risk Capital Charge Standardized CVA capital charge h = 1 (one-year horizon) Bi and Bind denote the hedging positions in single-name and indices The level and reasonableness of the standardised CVA risk capital charge, including a comparison to the advanced approach, is subject to a final impact assessment targeted for completion in the first quarter of

11 Wrong-Way Risk in Basel III Banks must identify exposures that give rise to general WWR Stress testing and scenario analyses to identify risk factors positively correlated with credit worthiness including severe shocks occurring when relationships between risk factors have changed Monitor general wrong way risk by product, by region, by industry, etc. Reports provided to senior management and Board on a regular basis Explicit Pillar I charge for identified specific WWR higher EAD Explicit procedure for identifying, monitoring and controlling specific WWR Instruments for which there is a legal connection between CP and underlying issuer and for which specific WWR has been identified are to be taken out of netting set with other transactions CDSs: use expected loss assuming underlying in liquidation (LGD for swap = 1%) Equity, bond, securities financing: EAD = value of transaction under JtD Analytical CVA and Contributions (Normal Approx.) Analytical expressions Contributions including wrong-way risk Need to modify the approach to obtain the contributions to the CP EE conditional on the CP defaulting For this purpose, we define a Normal copula V ( t) = µ ( t) + σ ( t) X i i i i Y =Φ Same results but instead of the unconditional expectations, standard deviations and correlations of the trade values, we now use the conditional ones ˆ µ ( t) E[ V ( t) τ = t ] = µ ( t) + σ ( t) bφ P( t) i i i i i ˆ σ ( t) StDev[ V ( t) τ= t ] = σ ( t) 1 b 2 i i i i ˆ ρ ( t) = i ρ ( t) bβ ( t) i i 2 2 (1 bi )[1 β ( t)] 1 [ ] 1 [ Pτ ( )] X by b X 2 1 ˆ i = i + i i

12 CCR Capital and Alpha Methodology (Garcia et al) Framework defined by two key components: Non-parametric sampling of exposures from pre-computed PFEs (unconditional) Direct modelling of codependence of and exposures and systematic credit factors (non-parametric exposures sampling also from joint market-credit factor scenarios) Computationally efficient fully leverages pre-computed PFE profiles Minimizes work during the most computationally intensive step Multiple capital calculations model validation, sensitivities, stress testing Model can be applied within general integrated market-credit risk models Stress testing Wrong-way risk and transparency of counterparty concentrations and factors driving exposures Market-credit correlations contrast to industry studies, conservative assumptions, or from a previously estimated market-credit risk model Wrong-Way Risk Correlated Market-Credit General market-credit codependence framework CP exposures (Simulated from market factors) Credit factors defaults Copula parameters: ρ Capital

13 Dan Rosen WWR Model at the Portfolio Level Integrated market and credit portfolio model Simulated jointly for entire portfolio Copula (X, Z) Codependence of exposures and credit events Exposures (market scenarios) E i = f ( X) i Credit events Y = ρ Z+ 1 ρ ε N PD( Z) = N 1 ( PD) ρ ρ 1 i z Syst. factor X Syst. factor Z Idiosyncratic CP factors Calculating CVA with Wrong-Way Risk CVA with WWR M j j ( 1 R) D ( tk) E ( tk) P( ω j, tk 1< τ tk) CVA < WWR = k j ( 1 R) eˆ ( tk) [ P( tk) P( tk )] CVAWWR = 1 Expected exposure conditional on default k eˆ M j j ( tk) = D ( tk) E ( tk) j ( ω, t < τ < t ) P P j ( t ) P( t ) k k 1 k 1 k Analytical formula for EPE default Explicit formula for the joint probability... But very expensive (large number of bi-normal distributions) Requires numerical evaluation Depends on the joint market-credit model and the correlation parameters Exposure ( Million) Counterparty PFE Mean Exposure 95 Percentile Cond. EPE Time (days)

14 Methods for Calculating CVA with WWR Conditioning on the default interval is computationally infeasible. Requires approximations: Fixed expected exposure at default (can be shown to be conservative) Linear Approximation: When simulating new PD scenarios, calculate CVA using a linear approximation (in PD) to the REP formula: CVA New = CVA Old + ( PD New PD Old ) CVA PD ( ) PD Old Calculating CVA with WWR Based on explicit computations of the derivatives, the linear approximation algorithm is quite fast One can show that (from the analytical formulas for the derivatives) that fixing the expected exposure at default will be conservative (aggressive) in the presence of wrong-way risk (right-way risk). CVA PD

15 Methods for Calculating CVA with WWR Conditioning on the default interval is computationally infeasible Conditioning directly on default exactly at time t k is faster : CVA i = (1 R i ) e ˆ * (t)dp i (t) ˆ e * (t)= E[D(t)E (t) τ = t] Avoids computation of cumulative bivariate normal distributions. Still requires significant computation (inverse normal distributions for each time, counterparty and simulation scenario) Accuracy could be a consideration if the time points are far apart Example: trapezoid Rule (conditioning on exact default time): K e ˆ * (t CVA (1 R i ) k )+ e ˆ * (t k 1 ) P(t k=1 k ) P(t k 1 ) 2 e ˆ * (t k )= D j (t k ) E j (t k ) P(ω j τ i = t k ) j T ( ) Remarks on WWR at the Portfolio Level Integrated market and credit portfolio model While the CVA is the sum of CP CVAs, we must use the same model and correlation parameters to compute CVA at the portfolio level Under a given model (market factor and correlation levels) not all CPs will simultaneously have WWR Stress testing of individual CPs can be done with different set of parameters Exposures E i = f Syst. factor X Copula (X, Z) Codependence of exposures and credit events ( X) i Syst. factor Z Credit events Y = ρ Z+ 1 ρ ε 1 N ( ) ( PD) ρ z PD Z = N 1 ρ Idiosyncratic CP factors i

16 % 7% 6% 5% 4% 3% 2% 1% 95% Percentile %5 Percentile Mean exp % Run of April, 28 (26/6/28) Exposure ('s) Counterparty (Top 7 mean exposures) 1.6 Base Case 1.7 Base Case 1.6 Average 1.5 Single Step Stress % Vol: Exposures 17.71% Average Mean / Vol: Multi-Steps 12 TS - MS / MS Mean Single Exposure Step Stress Statistics Exposures ('s) Multi-Steps 12 TS - MS Portfolio / MS Size Statistics Multi-Steps 59 TS - MS / MS Multi-Steps 12 TS - MS / SS 1.5 Multi-Steps 59 TS - MS / MS Multi-Steps 12 TS - MS / SS Multi-Steps 59 TS - MS / SS Multi-Steps 59 TS - MS / SS Top 1 Exposures (' Euros) No Counterparties: Counterparty Mean 95th Percentile 5th Percentile Sigma 1.4 No CP Exp Zero or Neg: - 1, A ,32 199,954 12, % Statistics for CP Exposure > 1 Euro 1 M EAD4TE 154, ,365 83, % Mean: 31, Effective Counterparty Number , ,864 12, % Median: 15, CRUPAR 98,58 116,262 79, % 1.1 STD: 33, ,41 11,398 8, % Kurtosis*: Y ,691 14,345 51, % 1. Skew*: ,931 91,878 78, %.9 Maximum : 158, ,592 9,347 7, % Largest(1): 59, KHBNYC 78,14 82,675 73, % Smallest(1): 8, No of.75 CPs 1 P ,223 74,456 44, % Minimum: 8, Client Confidential.25.5 Copyright.75 R2 Financial 1Technologies 27 Alpha (99.9%) as a function of market-credit correlation Alpha Total (LTS/LTD) Single Step Multi-Steps 12 TS - MS / MS MS / SS Multi-Steps 59 TS - MS / MS MS / SS Client Confidential Copyright R2 Financial Technologies 28 Alpha Systematic (LSS/LSD) Single Step Multi-Steps 12 TS - MS / MS MS / SS Multi-Steps 59 TS - MS / MS MS / SS Client Confidential Copyright R2 Financial Technologies Dan Rosen Case Study Sample portfolio: 7 counterparties Transactions: FI, FX, equity and credit derivatives (multiple currencies) PFE profiles - simulated over 3 years using 2, market scenarios and 21 time steps (MtF) Calibrated using historical data mean reversion for relevant parameters Alpha Alpha % Mean exposure Portfolio Exposure Summary: Regulatory Capital One-Year Equivalent Exposures One-Year Equivalent Mean Exposures Alpha (99.9%): Base Case vs. Stressed Exposures Run of April, 28 (26/6/28) Alpha (99.9%): Comparison Single vs Multiple Steps Alpha - Total (99.9%) Alpha - Systematic (99.9%) Alpha - Total (99.9%) Alpha Alpha - Systematic (99.9%) Alpha (99.9%) as a function of market-credit correlation Alpha Total (LTS/LTD) Base Case Stressed Exposures Alpha Systematic (LSS/LSD) Base Case Stressed Exposures Alpha Total Exposure: 2,176,463 Exposure > No of CP No of Eff CP HI No of Eff CP Frequency Portfolio Exposures Portfolio Exposure Summary: Regulatory Capital One-Year Equivalent Exposures One-Year Equivalent Mean Exposures 3% 25% 95% Percentile %5 Percentile Mean exp % Mean exposure 2% 15% 1% Frequency 5% % Counterparty (Top 7 mean exposures) Exposure ('s) Average % Vol: 17.71% Average Mean / Vol: 5.65 Mean Exposure Statistics ('s) Portfolio Size Statistics Total Exposure: 2,176,463 Exposure > No of CP No of Eff CP HI Top 1 Exposures (' Euros) No Counterparties: Counterparty Mean 95th Percentile 5th Percentile Sigma No CP Exp Zero or Neg: - 1, A ,32 199,954 12, % Statistics for CP Exposure Euro > 1 2 6EAD4TE 154, ,365 83, % Mean: 31,92 3 Effective Counterparty Number , ,864 12, % Median: 15, CRUPAR 98,58 116,262 79, % STD: 33, ,41 11,398 8, % Kurtosis*: Y ,691 14,345 51, % Skew*: ,931 91,878 78, % Maximum : 158, ,592 9,347 7, % Largest(1): 59, KHBNYC 78,14 82,675 73, % Smallest(1): 8, No of CPs P ,223 74,456 44, % Minimum: 8,53.13 Client Confidential Copyright R2 Financial Technologies 21 No of Eff CP

17 Dan Rosen Counterparty Level Exposures Counterparty Report: Exposure and CVA Run of December, 29 (18/1/21 CP level) Counterparty Info Counterparty A No of Instruments 111 Sector FINANCIALS Rating BBB+ PD.1367% LGD.4 Hazard Rate.24 HR Volatility.5 Asset Exposure Mean Exposure Cond. Mean Exposure 95 Percentile Counterparty Info Counterparty 6MPEBTQ CVA Stress Testing No of 3.4 Instruments Sector INDUSTRIALS 3.3 Rating BBB- PD.359% 1 LGD Hazard Rate.24 HR Volatility Asset Exposure Mean Exposure Cond Mean Exposure 95 Percentile Statistics ( million) Exposure Actual Exposure EPE Effective EPE Effective Maturity* 1.57 Total Capital 8.51 CVA Market-Credit Corr..25 CVA Unilateral 3.13 CVA Bilateral CVA Uncorrelated 3.6 Exposure ( Million) Time in Days CVA ( Million) 3. ( Million) Statistics ( million) 6 Exposure 2.9 Actual Exposure EPE Effective EPE Effective Maturity* Total Capital CVA Mkt- 2.6 Credit Corr..25 CVA Unilateral CVA Bilateral CVA Uncorrelated 1.31 CVA - WWR Stress Test ( million) Time in Days CVA Copyright R2 Financial Technologies 21 Copyright R2 Financial Technologies CCR Capital (Independent Market-Credit) CCR Losses and EC Report (Numbers in Million) Run of December, 29 (18/1/21) CCR Losses and EC Total (Stochastic) Loss Histogram Deterministic Stochastic Deterministic - Syst Stochastic - Sys VaR Frequency (Thousands) VaR 9% VaR 95% VaR 99% VaR 99.5% VaR 99.9% Quantile 2 OTC Derivatives Credit Capital (Simulation: 1M systematic scenarios) EL Capital Sigma VaR 9% VaR 95% VaR 99% VaR 99.5% VaR 99.9% ES 99.9% Det - SA Systematic Percent 1% 52% 54% 68% 62% 51% 54% 54% 55% Stoch - SA* Systematic Percent 1% 5% 52% 69% 62% 53% 51% 52% 53% * = Client Confidential Copyright R2 Financial Technologies

18 CCR Capital WWR Correlated Market-Credit Wrong-Way Risk CCR Capital Stress Test: Alpha (99.9%) 1.4 Alpha - Total (99.9%) 1.6 Alpha - Systematic (99.9%) 1.2 VaR Based 1.4 VaR Based 1. Capital Based 1.2 Capital Based Alpha.8.6 Alpha Alpha Multiplier by level at 99.9% (Between Exposures and Credit Events) Alpha Total (LTS/LTD) VaR Based Capital Based Alpha Systematic (LSS/LSD) VaR Based Capital Based Client Confidential R2 Financial Technologies 21 Copyright Alpha <1.2 correlations ~ 75% (Basel II) Negative correlations right-way exposures (alpha < 1.) Systematic alpha more sensitive to market-credit correlation (no idiosyncratic risk) CCR Capital WWR Correlated Market-Credit Exposure (millions) Exposures and Ordered Scenarios Run of December, 29 (18/1/21) Ordered Scenarios based on Total Exposure 9 88 Total Exposure Moving Avg. Trendline Ordered Scenario (First PC) Market factor correlated to defaults Important to understand why? Portfolio may have right-way or wrong-way exposures? may change over time In practice, can find smile effect some CPs are positively correlated and some negatively correlated Exposure factors include PCs, EL Total exposure (TE is generally the most conservative) Scenario Statistics Principal Components No Scenarios: 2, PC Explained Variation Maximum*: 1, First 69.6% Mean*: Second 14.95% Median*: Third 5.75% STD*: Minimum*: * million Client Confidential Copyright R2 Financial Technologies

19 CCR Regulatory Capital Internal Model Example 2: Stressed Exposures Alpha (99.9%): Base Case vs. Stressed Exposures Run of April, 28 (26/6/28) 1.7 Alpha - Total (99.9%) 1.8 Alpha - Systematic (99.9%) 1.6 Base Case 1.7 Base Case 1.5 Stress Exposures 1.6 Stress Exposures Alpha Alpha Alpha (99.9%) as a function of market-credit correlation Alpha Total (LTS/LTD) Base Case Stressed Exposures Alpha Systematic (LSS/LSD) Base Case Stressed Exposures Confidential Financial Technologies 28 Client Copyright R

20 % 7% 6% 5% 4% 3% 2% 1% Base Case 95% Percentile %5 Percentile Mean exp Run of April, 28 (26/6/28) Stress Exposures Stress Exposures % Single Step Multi-Steps 12 TS - MS / MS Single Step Multi-Steps 12 TS - MS / MS 1.5 Exposure ('s) Multi-Steps 59 TS - MS / MS Multi-Steps Counterparty 12 TS (Top - MS 7 / SSmean exposures) 1.5 Multi-Steps 59 TS - MS / MS Multi-Steps 12 TS - MS / SS Multi-Steps 59 TS - MS / SS 1.4 Multi-Steps 59 TS - MS / SS 1.3 Average % Vol: 17.71% Average Mean / Vol: Mean Exposure Statistics ('s) Portfolio Size Statistics Top 1 Exposures (' Euros) 1.2 No Counterparties: Counterparty Mean 95th Percentile 5th Percentile 1.2 Sigma1.1 No CP Exp Zero or Neg: - 1, A ,32 199,954 12, % Statistics for CP Exposure > 1 Euro 1 M EAD4TE 154, ,365 83, % Mean: 31,92 Effective Counterparty Number , ,864 12, % 1..9 Median: 15, CRUPAR 98,58 116,262 79, % STD: 33, ,41 11,398 8, % Kurtosis*: Y ,691 14,345 51, % Skew*: ,931 91,878 78, % Maximum : 158, , , , % Largest(1): , KHBNYC 78,14 82,675 73, % Smallest(1): 8,55.34 No of CPs P ,223 74,456 44, % Minimum: 8,53.13 Alpha (99.9%) as a function of market-credit correlation Client Confidential Copyright R2 Financial Technologies Alpha Total (LTS/LTD) Single Step Multi-Steps 12 TS - MS / MS MS / SS Multi-Steps 59 TS - MS / MS Client Confidential Copyright R2 Financial Technologies 28 MS / SS Alpha Systematic (LSS/LSD) Single Step Multi-Steps 12 TS - MS / MS MS / SS Multi-Steps 59 TS - MS / MS MS / SS Client Confidential Copyright R2 Financial Technologies Base Case Dan Rosen Empirical Market-Credit s Historical time series: market index, implied credit driver and default rates (S&P data) Historical Default Rates ( ) Def Rate ALL (%) Def Rate INV (%) X between all ratings and investment only Default rates = 78% Implied Credit factors = 7% between credit factor and market index All ratings = 23% Investment grade = 29% * EQ Index vs. ALL Grades Equity Index Systematic Credit factor Default Rate (%) EQ Index vs. Investment Grade Equity Index Systematic Credit factor default rate (%) X CVA Some Assumptions for CVA For simplicity, use same exposures as for CCR capital (not risk-neutral) Credit model Constant risk-neutral HR per rating (real PDs also per rating and higher than we have used in the past at BBVA) LGDs from spread pricing Asset correlation Basel II Base market-credit correlation =25% Market risk factors hazard rates (and not the spreads) Daily volatility returns 3-5% Flat market factor correlations 4% Alpha - Total (99.9%) Alpha (99.9%): Comparison Alpha - Systematic Single (99.9%) vs Multiple Steps Stand-alone VaR computed analytically, and simulation for portfolio VaR Alpha Alpha % Mean exposure One-Year Equivalent Exposures Alpha - Total (99.9%) Alpha One-Year Equivalent Mean Exposures Alpha (99.9%): Base Case vs. Stressed Exposures Run of April, 28 (26/6/28) Alpha - Systematic (99.9%) Alpha (99.9%) as a function of market-credit correlation Alpha Total (LTS/LTD) Base Case Stressed Exposures Alpha Systematic (LSS/LSD) Base Case Stressed Exposures Alpha Portfolio Exposure Summary: Regulatory Capital Total Exposure: 2,176,463 Exposure > No of CP No of Eff CP HI No of Eff CP Frequency

21 Dan Rosen Portfolio CVA Portfolio CVA Summary Portfolio Summary ( million) No of CPs 7 Mark-to-Market 2,291 Actual Exposure 3,882 EPE 2,176 CVA Unilateral 75.8 Bilateral Capital CCR Capital CVA VaR CVA Statistics ( million) Total CVA 75.8 Mkt-Credit Corr..25 Mean 1.8 Median.39 STD 2.57 Kurtosis* Skew* 5.95 Maximum Largest Smallest 1.1 Minimum.4 ( Million) CVA by Counterparty 78. CVA Stress Testing Counterparties CVA CVA Concentration ( Million) CVA - WWR Stress Test ( million) CVA Internationa l Corporates, Financials, Project Finance, Central Bank,.34 Large Domestic Corporates, 8.48 Other Corporates, Counterparty Exposure, CVA, and WWR Counterparty Report: Exposure and CVA Run of December, 29 (18/1/21 CP level) Counterparty Info Counterparty 6MPEBTQ No of Instruments 11 Sector INDUSTRIALS Rating BBB- PD.359% LGD.4 Hazard Rate.24 HR Volatility.5 Asset Exposure Mean Exposure Cond Mean Exposure 95 Percentile CVA Stress Testing Statistics ( million) Exposure Actual Exposure EPE 35.5 Effective EPE Effective Maturity* 2.81 Total Capital 3.44 CVA Mkt- Credit Corr..25 CVA Unilateral 1.36 CVA Bilateral CVA Uncorrelated 1.31 ( Million) (CVA Million) Time in Days CVA - WWR Stress Test ( million) CVA Copyright R2 Financial Technologies

22 CVA Market VaR Base Case Results Independent market and credit risk. 7.E+6 6.E+6 5.E+6 4.E+6 3.E+6 2.E+6 Fixed ExpEAD Full Internal Model (Trap) Linear Approximation 1.E+6.E+ VaR.9 VaR.95 VaR.99 VaR.995 VaR.999 CVaR

23 Stress Testing WWR 1-Day VaR at 99% confidence level, for various assumed levels of market-credit correlation. Fixed EDPE Full Internal Model Linear Approximation 5.1E+6 5.E+6 4.9E+6 4.8E+6 4.7E+6 4.6E+6 4.5E+6 4.4E+6 4.3E Capital Charges Standardized Capital Charge: m Internal model charges (millions) for different correlation levels: Capital =3 1 ( VaR 1 day,.99 +SVaR 1 day,.99 ) Base Case Stress Case Base Case : SVaR = VaR Stress Case : SVaR = 1.5 VaR

24 Concluding Remarks CVA and Wrong Way Risk CVA must be priced for derivatives portfolios the crisis showed its practical role and impact Conceptually simple, but complex problem in practice Consequences now reflected in accounting and capital rules We are just starting to understand its modelling and its financial, regulatory and management requirementsand impacts Wrong-way risk is important Portfolio effects may reduce its systematic impacts (general WWR) Specific WWR needs to be analyzed with stress testing and individual counterparty analysis Basel III regulation is not yet fully aligned with some of the best practices, but will likely move there over time

25 CVA and Model Risk CVA is pricing do we want to achieve pricing-level accuracy Marginal contributions, real time, securitization of CVA But how accurate can we. Or will we do it in the near future? This is probably the Most complex instrument we have ever priced! Complex risks Modelling CCR and CVA requires integrated market-credit models: 1s or 1s of market factors driving exposures over very long horizons Wrong-way risk Credit risk of portfolios of very complex and varied derivatives Mitigation: netting, collateral, margin calls. We cant price very well yet synthetic CDOs! Simple portfolios, standardized instruments, 125 credits Final Lessons Model risk framework Acknowledge the heroic assumptions in our models and the limitation of the information which we can reasonably extract from the market and quoted prices Effectively incorporate fundamental credit information, historical data and expert judgment into the valuation process Develop explicit model risk and stress testing approaches which can help us understand better The behaviour of instruments and portfolios, Knightean uncertainties we could be facing

26 Bio Dan Rosen Dan Rosen is the CEO and co-founder of and an adjunct professor of Mathematical Finance at the University of Toronto. Dr. Rosen lectures extensively around the world on financial engineering, enterprise risk and capital management, credit risk and market risk. He has authored several patents and numerous papers on quantitative methods in risk management, applied mathematics, operations research, and has coauthored two books and various chapters in risk management books (including two chapters of PRMIA s Professional Risk Manger Handbook). In addition, Dr. Rosen is a member of the Industrial Advisory Boards of the Fields Institute and the Center for Advanced Financial Studies at the University of Waterloo; the Academic Advisory Board of Fitch; the Advisory Board of the IAFE; a founder former Regional Director and current steering committee member of PRMIA in Toronto; and a member of the Oliver Wyman Institute. He is also one of the founders of RiskLab, an international network of research centers in Financial Engineering and Risk Management. Dr. Rosen was inducted in 21 as a fellow of the Fields Institute for Research in Mathematical Sciences, for his outstanding contributions to the Fields Institute, its programs, and to the Canadian mathematical community. Prior to co-founding R 2, Dr. Rosen had a successful ten-year career at Algorithmics Inc., where he held senior management roles in research and financial engineering, strategy and business development, and product marketing. In these roles, he was responsible for setting strategic direction, new initiatives and alliances; the design and positioning of credit risk and capital management solutions, market risk tools, operational risk, and advanced simulation and optimization, as well as their application to industrial settings. He holds an M.A.Sc. and Ph.D. in Chemical Engineering from the University of Toronto Selected Recent Publications Rosen D., 21, Rethinking Valuations, in Rethinking Risk Measurement (Ed. K. Boecker), RISK Publications Rosen D. and Saunders D. 211, Structured Finance Valuation and Risk Management with Implied factor Models, in Advances in Credit Derivatives, Bloomberg Publications Nedeljkovic, J., Rosen D. and Saunders D. 21, Pricing and Hedging CLOs with Implied Factor Models, Journal of Credit Risk, fall issue Rosen D. and Saunders D. 29, Valuing CDOs of Bespoke Portfolios with Implied Multi- Factor Models, Journal of Credit Risk, Fall Issue Rosen D. and Saunders D. 211, Wrong-Way CVA and CVA VaR, working paper Pykhtin M., Rosen D. 21, Pricing Counterparty Risk at the Trade Level and CVA Allocations, Federal Reserve Research Paper Series (Journal of Credit Risk) Rosen D. and Saunders D. 21, Computing and Stress Testing Counterparty Credit Risk Capital, in Counterparty Credit Risk Modelling, (ed. E. Canabarro), Risk Books Garcia Cespedes J. C., de Juan Herrero J. A., Rosen D., Saunders D. 21, Effective modelling of Counterparty Credit risk Capital and Alpha, Journal of Risk Model validation De Prisco B., Rosen D., 25, Modelling Stochastic Counterparty Credit Exposures for Derivatives Portfolios, Counterparty Credit Risk (M. Pykhtin, Editor), Risk Books

27 Selected Recent Publications Rosen D. and Saunders D. 21, Economic Capital, in Encyclopedia of Quantitative Finance Rosen D. and Saunders D. 21, Risk Contributions and Economic Credit Capital Allocation, in Advances in Credit Derivatives, Bloomberg Publications (forthcoming) Rosen D. and Saunders D. 21, Measuring Capital Contributions of Systemic Factors in Credit Portfolios, Journal of Banking and Finance Rosen D. and Saunders D. 29, Analytical Methods for Hedging Systematic Credit Risk with Linear Factor Portfolios, Journal of Economic Dynamics and Control Mausser H. and Rosen D. 27, Economic Credit Capital Allocation and Risk Contributions, in Handbook of Financial Engineering (J. Birge and V. Linetsky Editors) Garcia Cespedes J. C., Keinin A., de Juan Herrero J. A. and Rosen D. 26, A Simple Multi-Factor Factor Adjustment for Credit Capital Diversification, Special issue on Risk Concentrations in Credit Portofolios (M. gordy, editor) Journal of Credit Risk, Fall 26 Rosen D., 24, Credit Risk Capital Calculation, in Professional Risk Manager (PRM) Handbook, Chapter III.B5, PRMIA Publications Aziz A., Rosen D., 24, Capital Allocation and RAPM, in Professional Risk Manager (PRM) Handbook, Chapter III., PRMIA Publications