Counterparty Credit Risk and CVA under Basel III

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Financial institutions which apply for an IMM waiver under Basel III need to fullfill a broad set of requirements. We present the quantitative, organizational and operational implications and provide some hand-on guidance how to fulfill the regulatory requirements.

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Counterparty Credit Risk and CVA under Basel III

  1. 1. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Counterparty Credit Risk and CVA under Basel III Patrick H¨aner H¨aner Consulting Berlin c 2015 H¨aner Consulting CCR&CVA under Basel III 1 / 205
  2. 2. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Outline 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 2 / 205
  3. 3. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Motivation Definition (Credit Risk) Risk to incur a loss due to counterparty’s default or loss of creditworthiness. Credit risk measures are introduced to Quantify the credit risk Help Mitigating that risk c 2015 H¨aner Consulting CCR&CVA under Basel III 3 / 205
  4. 4. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Motivation Risk measures are estimated by Credit Risk Models Impact of Credit Risk Model Trading activity limits set by PE Capital charges regularity capital dependent of EEPE P&L EE enters CVA/DVA c 2015 H¨aner Consulting CCR&CVA under Basel III 4 / 205
  5. 5. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Motivation Challenges Measure Asking the right question Model Picking right model to estimate measure Act Make descisions based on measurements c 2015 H¨aner Consulting CCR&CVA under Basel III 5 / 205
  6. 6. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Overview 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 6 / 205
  7. 7. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Likeliness vs Severity of Credit Events Categories Which dimensions to consider? Severity How much will we lose? Likeliness What’s the chance that we lose? Granularity What does the measure refer to? c 2015 H¨aner Consulting CCR&CVA under Basel III 7 / 205
  8. 8. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Granularity of Measure Based on Defaults All Counterparties Single Counterparty Other Aggregations Global/macro economic Sector, country Trade c 2015 H¨aner Consulting CCR&CVA under Basel III 8 / 205
  9. 9. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Exposure and Recovery How to measure severity? Need to value trade: Definition (Exposure at Default) EAD(t) = max 0, p(t)|τ = t τ : time at which CP defaults Definition (Loss Given Default) Loss at time t = LGD(t)EAD(t) Definition (Recovery) R(t) = 1 − LGD(t) c 2015 H¨aner Consulting CCR&CVA under Basel III 9 / 205
  10. 10. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Severity Valuation Approaches Accrual Banking book; rarely adjust; illiquid assets Mark to market Trading book; frequently adjusted; traded assets Mark to model Trading book; frequently adjusted; complex structures Example CreditRiskMeasures.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 10 / 205
  11. 11. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Severity Accrual Loan to Acme Ltd value is face value maximal loss is notional of loan Mark to market Buy bond of Acme Ltd; assume liquid market value is mark to market of bond value lower than in risk-free valuation c 2015 H¨aner Consulting CCR&CVA under Basel III 11 / 205
  12. 12. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Severity Mark to model Exotic interest rate swap with Acme Ltd. What is the value risk free: assuming Acme may never default risky: Acme may default risky with own risk: Acme and we may default c 2015 H¨aner Consulting CCR&CVA under Basel III 12 / 205
  13. 13. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Forward Looking Measures Assess exposure in future → model how state of the world evolves Deterministic Evolution Scenario Analysis, Stress testing Stochastic Evolution Model for risk factors c 2015 H¨aner Consulting CCR&CVA under Basel III 13 / 205
  14. 14. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Scenario Analysis/Stress Test Meanings of Stress change model parameters → pick a single path → degenerate measure (Dirac measure) Unified handling by Measure Transforms Stochstic Process (Langevin Equation) Dual Model Representations Probabiliy Measure (Path Integrals) : t ! x(t) Path µ( ) ⇠ e S( ) S( ) ⌘ Z ⌧ 0 L(x, ˙x) Action L(x, ˙x) : Lagrangian ˙x = f(x) + ⇠ c 2015 H¨aner Consulting CCR&CVA under Basel III 14 / 205
  15. 15. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Types of Stress Tests Approaches give economic scenario given loss (inverse stress) Inverse stresses c 2015 H¨aner Consulting CCR&CVA under Basel III 15 / 205
  16. 16. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Statistical Measures Single Netting Set Definition (Potential Future Exposure) PFE(t) = max 0, p(t)|τ = t τ : time at which CP defaults Definition (Expected Exposure (EE)) EE(t) = E[PFE] Definition (Expected Positive Exposure) EPE(T) = 1 T T 0 EE(t) dt c 2015 H¨aner Consulting CCR&CVA under Basel III 16 / 205
  17. 17. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Regulatory Measures Definition (Effective Expected Exposure (EEE)) Maximum of EPE and past EEE: never decreasing. c 2015 H¨aner Consulting CCR&CVA under Basel III 17 / 205
  18. 18. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Statistical Measures Multiple Netting Set Definition (Losses across Netting Sets) L(t) = a χτa≤tLGDa max 0, pa(τa) a : Identifier of netting set c 2015 H¨aner Consulting CCR&CVA under Basel III 18 / 205
  19. 19. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Portfolio Measures Meaningful risk measures for portfolios Definition (Coherent Risk Measure) Risk measure ρ: for portolio X: Normalization ρ(∅) = 0 empty portfolio has no risk Monotonicity X1 ≤ X2 → ρ(X1) ≥ ρ(X2) Sub-additivity ρ(X1 + X2) ≤ ρ(X1) + ρ(X2) diversification/netting Homogeneity ρ(αX) = αρ(X) α > 0 Translation invariance ρ(X + a) = ρ(X) − a adding cash a reduces risk c 2015 H¨aner Consulting CCR&CVA under Basel III 19 / 205
  20. 20. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Portfolio Measures Quantile q% quantile: value, for which q% of outcomes are smaller/larger. Quantiles are not coherent measures. Expected Shortfall Expected loss conditioned on the loss being larget than X. The Expected Shortfall (Mean Excess Loss) is a coherent measure. Example PortfolioMeasure.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 20 / 205
  21. 21. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Likeliness of Default Example LikelihoodExperiment.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 21 / 205
  22. 22. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk What does probability mean? Average observers Implied ensemble Genuine ensemble Probability and Measurement Need to define Ensemble Measurement process c 2015 H¨aner Consulting CCR&CVA under Basel III 22 / 205
  23. 23. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Examples Genuine Ensemble Mathematics Physics: Identically prepared experiment Average observers Consensus of observers: Market prices Betting quota Implied Ensemble Equivalence classes: Names with same rating Price returns in different time windows c 2015 H¨aner Consulting CCR&CVA under Basel III 23 / 205
  24. 24. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Measures for Probability of Default Definition (Survival/Default Probability, Default Intensity) Let τ be time of default S(t) = p(τ > t) S : survival probability S(t) = e−λ(t)t λ : term default intensity D(t) = 1 − S(t) D : default probability Note: D is a CDF! c 2015 H¨aner Consulting CCR&CVA under Basel III 24 / 205
  25. 25. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Forward Intensity Forward default intensity Probability d(t) of defaulting between t and dt: d(t) = dD(t) dt (1) c 2015 H¨aner Consulting CCR&CVA under Basel III 25 / 205
  26. 26. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Estimating Probability of Default Estimating λ Credit Rating Typically using historical data Market Prices Current credit spreads from bonds or CDS Implied Default Intensity Let s(t) be a credit spread s(t) = (1 − R)λ(t) R : recovery rate c 2015 H¨aner Consulting CCR&CVA under Basel III 26 / 205
  27. 27. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Unifiying Severity and Frequency Measures High Severity/Low Frequency vs. Low Severity High Frequency How to compare Single large deal with good counterparty Set of small deals with bad counterparties Answer Pricing including credit risk allows comparing! c 2015 H¨aner Consulting CCR&CVA under Basel III 27 / 205
  28. 28. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Approaches Top-down vs Bottom-up Top-down Pricing from first principles Bottom-up Calculate price correction from building blocks: Exposure (EE) and PE, LGD c 2015 H¨aner Consulting CCR&CVA under Basel III 28 / 205
  29. 29. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Bottom-Up approach Assumptions Risk-free prices known Calculate EE Estimate PE, LGD Calculate correction to risk-free price c 2015 H¨aner Consulting CCR&CVA under Basel III 29 / 205
  30. 30. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Measuring the Corrections Riskiness of counterparty reduces the price: Definition (CVA) Risky price p∗ A as seen from counterparty A with counterparty B: p∗ = p − CVAB p : risk-free price CVAB : Credit Valuation Adjustment for counterparty B c 2015 H¨aner Consulting CCR&CVA under Basel III 30 / 205
  31. 31. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Measuring the Corrections Does credit risk of counterparty A also affect price? Definition (DVA) Price pA as seen from counterparty A with counterparty B: p∗ = p − CVAB + DVAA p : risk-free price DVAA : Debit Valuation Adjustment for counterparty A DVA increases the price. Accounting vs. Regulatory DVA must be used for P&L but not for regulatory capital. c 2015 H¨aner Consulting CCR&CVA under Basel III 31 / 205
  32. 32. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Regulatory CVA BCBS 189, paragraph 89: Regulatory CVA Similar to regulatory capital charge for default: Assumes independence of exposure and default process. CVA = T 0 (1 − R)Df (t)EE(t)d(t) dt where d is the default probability from equation (1),Df discount factor c 2015 H¨aner Consulting CCR&CVA under Basel III 32 / 205
  33. 33. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk CVA Example CVA.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 33 / 205
  34. 34. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Regulatory CVA Regulatory vs Trading CVA Regulatory Historic measure for EE, implied for PD Trading Both EE and PD in implied measure c 2015 H¨aner Consulting CCR&CVA under Basel III 34 / 205
  35. 35. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Pricing for Portfolio of Netting Sets As for single netting sets: pricing combines severity and likeliness. Requires knowing prices of individual netting sets at default probability of default P(χτ1≤t1 , χτ2≤t2 , . . . , χτN ≤tN ) Additional useful quantity: in terms of total losses: Definition (Loss distribution) L(l, t) = P(L(t) ≥ l) c 2015 H¨aner Consulting CCR&CVA under Basel III 35 / 205
  36. 36. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Types of Measures Severity Frequency Pricing Credit Risk Granularity of Measure in Regulatory Context Metrics used for Regulatory Purposes Focus on measures for individual counterparties. No proper modelling of collective losses required. c 2015 H¨aner Consulting CCR&CVA under Basel III 36 / 205
  37. 37. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Overview 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 37 / 205
  38. 38. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Mitigate realized losses from default of counterparty P&L fluctuation from change in credit spreads of counterparty c 2015 H¨aner Consulting CCR&CVA under Basel III 38 / 205
  39. 39. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Netting Agreement Definition (Netting Set) For all trades within a netting set long and short positions may be netted. The exposure is reduced due to max i pi , 0 ≤ i max pi , 0 Example A short and a long position worth 10 Mios with counterparty acme yield an exposure of 10 Mio w/o netting agreement and 0 with. c 2015 H¨aner Consulting CCR&CVA under Basel III 39 / 205
  40. 40. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting CSA ISDA Credit Support Annex (CSA) : collateral that must be delivered between the parties Definition the Secured Party’s Exposure plus the aggregate of all Independent Amounts applicable to the Pledgor, minus all Independent Amounts applicable to the Secured Party, if any, minus the Pledgor’s Threshold The Secured Party is the party that is holding collateral; the Pledgor is the party that has delivered collateral c 2015 H¨aner Consulting CCR&CVA under Basel III 40 / 205
  41. 41. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting CSA MtM 0 IA(A) IA(B) T(B) Collateral held At default losses offset by collateral Rebalancing needed Collateral price may move c 2015 H¨aner Consulting CCR&CVA under Basel III 41 / 205
  42. 42. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Re-hypothecation Counterparty may repo the collateral → when defaulting collateral gone Forbidding may increase costs Transferring collateral management to central counterparty c 2015 H¨aner Consulting CCR&CVA under Basel III 42 / 205
  43. 43. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Gap Risk Collateral process is discreet, e.g. daily. position value collateral value may move c 2015 H¨aner Consulting CCR&CVA under Basel III 43 / 205
  44. 44. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Central Counterparties Counterparty to every trade Multiateral netting → reducing risk Potentially mutualizing credit losses among participants Increased transparency c 2015 H¨aner Consulting CCR&CVA under Basel III 44 / 205
  45. 45. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Spread vs Default Risk Definition (Default Risk) Risk of changes in price p induced by hitting default time τ: t → τ p → p + ∆τ p ∆τ p = (R − 1)p Definition (Spread Risk) Risk of changes in price p induced by changes of counterparty credit spread s: s → s + ∆s p → p + ∆sp ∂pc 2015 H¨aner Consulting CCR&CVA under Basel III 45 / 205
  46. 46. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Spread vs Default Risk Hedging Loans Default Risk Single name CDS or short bond Spread Risk MtM accounting Single name CDS/bond, index or proxy Accrual accounting N/A c 2015 H¨aner Consulting CCR&CVA under Basel III 46 / 205
  47. 47. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Hedging Instruments and Strategies Static Hedges Insurance for replacement of some asset on default: Bond hedged by Credit Default Swap Swap, CCYSwap Contingent Credit Default Swap (CCDS) Netting sets insurance from CVA desk Dynamic Hedges Hedging default or spread risk: use instruments with price q. First order: Default ∆τ q = −∆τ p Spread ∆sq = −∆sp c 2015 H¨aner Consulting CCR&CVA under Basel III 47 / 205
  48. 48. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Cross Counterparty Hedges Analogy Hedging Credit Risk for Bonds Granularity Underlying Hedge Single Bond CDS Netting Set CCDS Portfolio Bonds CDO Netting Sest ”CCDO” c 2015 H¨aner Consulting CCR&CVA under Basel III 48 / 205
  49. 49. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Securitisation Hedging losses across netting sets: CDO on CVA bond↔exposure of netting set tranches like CDO Issues notional of ”bond”s fluctuating ”bond” not transparent who rates the ”bond”s and the CDO? c 2015 H¨aner Consulting CCR&CVA under Basel III 49 / 205
  50. 50. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Systemic Risks In distressed market environment correlations increase → less diversification. Macro hedges Buying insurance won’t work (→ Monolines) c 2015 H¨aner Consulting CCR&CVA under Basel III 50 / 205
  51. 51. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Limit Monitoring Limits Manage size of exposure per counterparty industry region Limits may typically expressed in terms of Quantiles E.g. 95% quantile: 5% of losses are larger than that quantile Mean Expess Loss E.g. Average of the 5% biggest losses A term structure of limits may be reflect risk appetite. c 2015 H¨aner Consulting CCR&CVA under Basel III 51 / 205
  52. 52. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Mutualization Central Counterparties Losses distributed among participants → diversification Systemic risks? c 2015 H¨aner Consulting CCR&CVA under Basel III 52 / 205
  53. 53. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Trading CVA Trading desk within the firm: Sells default protection to other desks Hedges counterparty credit spread risk Costs/Benefits High build and run costs ⊕ More accurate metrics for credit risk ⊕ Increased transparency on costs ! Hegdges bought from CVA desk yield no regulatory capital relief c 2015 H¨aner Consulting CCR&CVA under Basel III 53 / 205
  54. 54. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Operating Model Mandate Depends on rationale for setting up Risk management or front office function? Responsibility often changes with sophistication . . . c 2015 H¨aner Consulting CCR&CVA under Basel III 54 / 205
  55. 55. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Responsibility c 2015 H¨aner Consulting CCR&CVA under Basel III 55 / 205
  56. 56. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Profit Centre vs Service Centre Approach Advantages Disadvantages Profit Centre P&L enable performance to be measured Easy to align renumeration with success and design incentives Potential conflicts of iterest May lead to overactive position taking Requires more infrastructure Service Centre Requires less infrastructure Less market activity Less internal politics Qualitative focus can lead to broader focus Difficult to measure performance Harder to retain and incentivise appropriate staff c 2015 H¨aner Consulting CCR&CVA under Basel III 56 / 205
  57. 57. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Methodology c 2015 H¨aner Consulting CCR&CVA under Basel III 57 / 205
  58. 58. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Methodology Risk vs pricing models: Use same models? Pricing model Fit market prices Risk model Predict future outcomes Bilateral vs unilateral calculation: Include products w/o PFE (e.g. notes) Define proxy spreads when no liquid CDS market Wrong way risk c 2015 H¨aner Consulting CCR&CVA under Basel III 58 / 205
  59. 59. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Infrastructure c 2015 H¨aner Consulting CCR&CVA under Basel III 59 / 205
  60. 60. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk System Requirements Basic requirements same as Monte Carlo Credit Risk system for Risk/Regulatory capital Additional Requirements Calulation of sensitivities Include wrong way risk in price Simulate in risk neutral calibration Integration with FO infrastructure and processes Attribution ability c 2015 H¨aner Consulting CCR&CVA under Basel III 60 / 205
  61. 61. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Netting Agreements Collateralization Hedging Limiting Internal CVA Desk Infrastructure Pre-trade approval/marginal CVA/DVA calculation: Needs to be fast Avoid recalculating whole portfolio: add new trades in scenario-consitent manner c 2015 H¨aner Consulting CCR&CVA under Basel III 61 / 205
  62. 62. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Overview 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 62 / 205
  63. 63. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Building Blocks Model Building Process Business Analysis Materiality, specification Model choice Find adequate model Software implementation Develop and roll out c 2015 H¨aner Consulting CCR&CVA under Basel III 63 / 205
  64. 64. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Materiality What to Model? Which risk factors material for current portfolio? How can we assess materiality without exposure model in place? Approach Simple estimation of exposure assuming future portfolio prices normally distributed estimation of first two moments c 2015 H¨aner Consulting CCR&CVA under Basel III 64 / 205
  65. 65. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Gaussian Approximation Need to estimate E[p(T)], E[p2(Ti )] at some future times T: Performing Taylor expansion for price p around expected risk factor: p(x(T), T) ≈ p(x0(T), T) + i ∂p(x0(T), T) ∂xi ∆xi (T) + 1 2 ij ∂2p(x0(T), T) ∂xi ∂xj ∆xi (T)∆xj (T) x0(T) ≡ E[x(T)] ∆xi (T) ≡ xi (T) − x0,i (T) c 2015 H¨aner Consulting CCR&CVA under Basel III 65 / 205
  66. 66. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Gaussian Approximation The expectation value M of the price is hence M(T) ≈ p(x0(T), T) + 1 2 ij γij (T)Ωij (T) M(T) ≡ E[p(x(T), T)] γij (T) ≡ ∂2p(x0(T), T) ∂xi ∂xj Ωij (T) ≡ E[∆xi (T)∆xj (T)] For the variance V we obtain up to second order in ∆x: V (T) ≈ ij δi (T)δj (T)Ωij (T) V (T) ≡ E[(p(x(T), T) − E[p(x(T), T)])2 ] δi (T) ≡ ∂p(x0(T), T) ∂xic 2015 H¨aner Consulting CCR&CVA under Basel III 66 / 205
  67. 67. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Gaussian Approximation What can we learn? Risk factor contributions Matrix elements Ψij = δi (T)δj (T)Ωij (T) indicate contribution of risk factors ij to total variance. EE, PE Knowning mean and variance of the Gaussian distribution, any statistical quantity may be evalued. Caveat Depending on specifics of portfolio this approximation may be more or less accurate: that is why we use Monte Carlo simulations after all. c 2015 H¨aner Consulting CCR&CVA under Basel III 67 / 205
  68. 68. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Practical Implementation For t = 0: δ and γ from Market risk system. But: need netting set level aggregation → deal level granularity For t > 0 estimate future δ, γ by bumping c 2015 H¨aner Consulting CCR&CVA under Basel III 68 / 205
  69. 69. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Requirements Represent trades/products Standardize for interoperability c 2015 H¨aner Consulting CCR&CVA under Basel III 69 / 205
  70. 70. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Trade Parameters Product represented by parameters FpML c 2015 H¨aner Consulting CCR&CVA under Basel III 70 / 205
  71. 71. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Trade Parameters Pro/Con ⊕ standardized logic in client c 2015 H¨aner Consulting CCR&CVA under Basel III 71 / 205
  72. 72. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Cashflows Product represented by casflows Payoff macros c 2015 H¨aner Consulting CCR&CVA under Basel III 72 / 205
  73. 73. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Cashflows Pro/Con ⊕ simple not expressive enough (just cash is exchanged) single product (no interations) c 2015 H¨aner Consulting CCR&CVA under Basel III 73 / 205
  74. 74. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Trade Models Transaction Model Approach Multi agent simulation: Time Map wall clock to simulation time Market Events simulation time to events Transactions events to transactions (e.g. cashflows) Execution execute events Pro/Con ⊕ general ⊕ all business logic in model → easy tooling expensive c 2015 H¨aner Consulting CCR&CVA under Basel III 74 / 205
  75. 75. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Criteria for Model Choice Categories Independent of product Relate to Mathemathics or Physics Dependent of product Specific to product type Dependent of portfolio and market Context c 2015 H¨aner Consulting CCR&CVA under Basel III 75 / 205
  76. 76. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Independent of Product Coordinate Sytems From Physics we know: dynamics must not depend on choice of coordinates → dimension analysis. Interpolation How to interpolate r, σ. Interpolate dimension-less quantities: rt and σ2t. c 2015 H¨aner Consulting CCR&CVA under Basel III 76 / 205
  77. 77. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Product Dependent State Variables vs. Parameters Liquidity Hedge frequency, transaction costs, close-out period Completeness Unhedgeable risk, uniqueness of price c 2015 H¨aner Consulting CCR&CVA under Basel III 77 / 205
  78. 78. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models State Variables and Parameters Indicators of Model Quality Parameter Dimensionality Avoid overparamerization Stability of Parameters Frequent recalibration: indicator of poor model performance GBM w termstructure vs Garch TS GBM Garch dimension ∞ 3 recalibration frequently for short end less frequent time-homogeneous N Y c 2015 H¨aner Consulting CCR&CVA under Basel III 78 / 205
  79. 79. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Arbitrage Risk Model for Volatility surface Directly modelling surface w/o arbitrage not trivial. Alternatively model option prices with HJM-like framework. c 2015 H¨aner Consulting CCR&CVA under Basel III 79 / 205
  80. 80. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Market Liquidity & Completeness Liquidity Hedge frequency, transaction costs, close-out period Completeness Unhedgeable risk, uniqueness of price c 2015 H¨aner Consulting CCR&CVA under Basel III 80 / 205
  81. 81. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Comparing Models Assume state of the world evolves randomly: Model as Process: Stochastic Differential Equation (Langevin Equation) dx dt = f (x) + g(x)ξ(t) Physics Notation dx = f (x)dt + g(x)dW (t) Finance Notation Wiener Process (SDE) dx = dW (t) W : Wiener Process c 2015 H¨aner Consulting CCR&CVA under Basel III 81 / 205
  82. 82. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Comparing Models Model as Measure P P : Γ → µ(Γ) probability Γ : t → x(t) some path Wiener Process (SDE) Γ ≡ {x1, . . . xN} µ(Γ) ∼ i G(xi , xi+1) G : Gaussian c 2015 H¨aner Consulting CCR&CVA under Basel III 82 / 205
  83. 83. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing & Risk Models Parametric Models Error Analysis Infer from parameter uncertainty price/risk uncertainty. Parameter Uncertainty E.g. such that hedging instrument prices still in bid-ask Parameter Error Uncertainty of price/risk due to error in parameters GBM with vol uncertainty (∆p)2 = ∂p ∂σ ∆σ 2 c 2015 H¨aner Consulting CCR&CVA under Basel III 83 / 205
  84. 84. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Benchmarking Pricing/risk factor models Q, Q , empirical measure P Comparing Pricing Models Q vs Q Risk Models P vs Q c 2015 H¨aner Consulting CCR&CVA under Basel III 84 / 205
  85. 85. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Benchmarking Distances How far apart two models? Need to define metric: Expectation values E.g. differences of prices and EEs under different measures Distributions E.g. Kullback-Leibler entropy dP P log dP P dP. Independent of quantity to average. c 2015 H¨aner Consulting CCR&CVA under Basel III 85 / 205
  86. 86. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Model Uncertainty Benchmarking giving limited answer: Calibration-Consistent Measures Define metric d to quantify goodness of calibration: pP i : model price calibration instrument i pi : market price calibration instrument i dP = i (pP i − pi )2 C = {P|dP ≤ } c 2015 H¨aner Consulting CCR&CVA under Basel III 86 / 205
  87. 87. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Model Uncertainty Non-uniqueness For d = 0: Multiple measures For single parametric measure, multiple solutions for calibration → ill behaved Incomplete market For d > 0: For single parametric measure: parameter risk c 2015 H¨aner Consulting CCR&CVA under Basel III 87 / 205
  88. 88. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Beyond Benchmarking Pricing model descriptive: Replicates prices of hedging instruments Determines no-arbitrage price of illiquit product How to asses quality of model? There are implied predictions: State variables vs parameters Prediction: parameters are constant Martingale Total price of deal and self-financing hedges should be 0 at any point in time c 2015 H¨aner Consulting CCR&CVA under Basel III 88 / 205
  89. 89. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development State variables and parameters State variables Temporal evolution or measure Parameters Family of evolutions/measures Analysis Choice of state variables: qualitative assessment Robustness of parameters: predicted are no changes c 2015 H¨aner Consulting CCR&CVA under Basel III 89 / 205
  90. 90. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Hedge Performance If perfectly hedged: pathwise replication → P&L distribution Unbiased Sharply peaked (Dirac) Hedge Simulations Self Consistency Use state variables simulated with pricing model Performance Historical state variables c 2015 H¨aner Consulting CCR&CVA under Basel III 90 / 205
  91. 91. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Exposure Goal Estimate Credit Risk measures → need to estimate exposure/price distributions in future. The exposure e(t) at time t of a netting set is given by e(t) = max 0, i pi (x, t) − C(t) (2) where pi price of trade i x risk factors C(t) price of collateral c 2015 H¨aner Consulting CCR&CVA under Basel III 91 / 205
  92. 92. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Calculating Exposure, CVA/DVA and Losses Risk Factors&Counterparty Default Times t x t x RT1 RT2 Risk Factors Trades t x t x R1 R2 Collaterals Portfolio Prices t p t p P1 P2 Collateral Prices t c t c C1 C2 PDF of Exposures Default Times of Counterparties PDF of Exposures at Default Expected Exposure Potential Future Exposure Bootom-up CVA/DVA Top-down CVA/DVA c 2015 H¨aner Consulting CCR&CVA under Basel III 92 / 205
  93. 93. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Building Blocks Components Required for estimating risk measures for single and portfolios of netting sets: Pricing Risk-factor Collateral Netting Dependency c 2015 H¨aner Consulting CCR&CVA under Basel III 93 / 205
  94. 94. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing Models Requirements Need to be fast! Ideally same as front office Perform well under stressed state variables c 2015 H¨aner Consulting CCR&CVA under Basel III 94 / 205
  95. 95. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing Models Acceleration Techniques Dumb lookup Approximate price as function of few variables define variables (e.g stock price) define grid recaluclate for each gridpoint price interpolate c 2015 H¨aner Consulting CCR&CVA under Basel III 95 / 205
  96. 96. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Pricing Models Acceleration Techniques Smart lookup Approximate price as function of few variables define variables (e.g stock price) prices on grid are side effect of pricing at spot; e.g. pricing on tree or AMC interpolate c 2015 H¨aner Consulting CCR&CVA under Basel III 96 / 205
  97. 97. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Risk Factor Models Pricing vs Risk Models Purpose Pricing Model Fit liquid market instruments; arbitrage-free Risk Model Predict Challenges for Risk Model Dependency Simultaneously simulate all asset classes Calibrationl Global calibration c 2015 H¨aner Consulting CCR&CVA under Basel III 97 / 205
  98. 98. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Risk Factor Models Short vs Long term prediction Long term prediction a challenge: Reducing dimensionality Economic macro factors Co-integration c 2015 H¨aner Consulting CCR&CVA under Basel III 98 / 205
  99. 99. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Risk Factor Models Pricing model Dynamics Arbitrage-free models used with risk calibration GBM HJM type of models ⊕ Well understood, tractable Not intended for risk c 2015 H¨aner Consulting CCR&CVA under Basel III 99 / 205
  100. 100. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Gaussian Dependency Modelling Goal Express random vector ξ with correlated ξi as linear combination of uncorrelated random factors ηi : ξ = Mη E[ξi ξj ] − E[ξi ]E[ξj ] ≡ Ωij E[ηi ηj ] − E[ηi ]E[ηj ] = λ2 i δij diagonal, pos. sem. def. What to consider? Ω? correlation matrix? c 2015 H¨aner Consulting CCR&CVA under Basel III 100 / 205
  101. 101. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Principal Component Analysis Dimensional Analysis Risk factors ξi not dimension-less! interest rate :[T−1] stock price :[Cash] volatility: [T−1 2 ] → Ωij may have different dimensions,i.e. Ω in general not a physically meaningful quantity! c 2015 H¨aner Consulting CCR&CVA under Basel III 101 / 205
  102. 102. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Principal Component Analysis Solution Consider instead of Ω following matrix Φ: Φij ≡ ∂f (ξ) ∂ξi ∂f (ξ) ∂ξj Ωij f : some function For dimensionality [Φ]: [Φij ] = [f ] [ξi ] [f ] [ξj ] [ξi ][ξj ] = [f 2 ] ∀i, j (3) c 2015 H¨aner Consulting CCR&CVA under Basel III 102 / 205
  103. 103. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development GBM Risk Factor Model Multivariate GBM Xi (t + ∆t) = Xi e(µi −1 2 σi )∆t+σi √ ∆tξi (t) µ : drift σ volatility ξi : Normal random Cov(ln Xi (t + ∆t), ln Xj (t + ∆t)) = Ωij c 2015 H¨aner Consulting CCR&CVA under Basel III 103 / 205
  104. 104. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Dependent Gaussian Random Variables Given uncorrelated Gaussian random number vector ζ. Need build η: Cov(ηi , ηj ) = Ωij c 2015 H¨aner Consulting CCR&CVA under Basel III 104 / 205
  105. 105. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Calibration Definition Calibration is the process to determine model parameters. Approaches Statistical Using historical data Implied Market implied parameters Economic Macro economical relation between rates, infaltion Asumptions Statistical Past is good predictor for future Implied Information in spot market predicts future Economic Some fundamental economic laws rule future c 2015 H¨aner Consulting CCR&CVA under Basel III 105 / 205
  106. 106. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Statistical Calibration For simple models: ad hoc parameter estimation averaging fitting Example SimpleEstimation.xls c 2015 H¨aner Consulting CCR&CVA under Basel III 106 / 205
  107. 107. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Maximum Likelihood Estimation Systematic way to calibrate Approach Parametric model with parameters α ↔ parametric measure µα: µα(Γ) = e−Sα(Γ) D[Γ] Assume: historical path ΓH is the most likely one. Find α∗ such that: µα∗ (ΓH) = max α µα(ΓH) c 2015 H¨aner Consulting CCR&CVA under Basel III 107 / 205
  108. 108. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Maximum Likelihood Estimation Implementation Assuming iid: µα(Γ) = m(xi ) m(x) = e−s(x) Γ = {x1, . . . , xn} Maximizing m ↔ minimizing i s(xi ) : log-likelihood c 2015 H¨aner Consulting CCR&CVA under Basel III 108 / 205
  109. 109. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Maximum Likelihood Estimation Example MLE.xls c 2015 H¨aner Consulting CCR&CVA under Basel III 109 / 205
  110. 110. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Implied Parameters Apply parameters used for pricing: Drift and Volatility Drift µ from T forward price (Covered Parity) Volatility σ T years ATM implied volatility Assumption Risk neutral measure yield good predictor for real-world measure Caveat Carry trades Supply/demand, risk premium Perform analysis before using implied parameters! c 2015 H¨aner Consulting CCR&CVA under Basel III 110 / 205
  111. 111. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Economic Calibration Parities connect for instance FX rates Inflation rates Real interest rates Nominal interest rates Purchansing power Example Parities.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 111 / 205
  112. 112. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Parities Example (Relative Purchasing Power Parity) pf (t1)(1 + if )X(t2) = pd (t2)(1 + id ) pd/f : domestic/foreign price id/f : domestic/foreign 1 yr inflation rate X : Exchange rate Yields after averaging E[X(t2)] X(t1) = 1 + Id 1 + If where I is the expected inflation rate. c 2015 H¨aner Consulting CCR&CVA under Basel III 112 / 205
  113. 113. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Parities Example (International Fisher Effect (Uncovered Parity)) (1 + rd/f ) = (1 + ρd/f )(1 + id/f ) rd/f : domestic/foreign nominal 1 yr interest rate ρd/f : real rdomestic/foreign 1 yr interest rate Assumingρd = ρf gives E[X(t2)] X(t1) = 1 + rd 1 + rf c 2015 H¨aner Consulting CCR&CVA under Basel III 113 / 205
  114. 114. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Issues with standard GBM model Issues rigidity: calibration short vs long horizons → term structure of parameters dimensionality → factor models underestimation of rare events and bursts (clustering) → GARCH not suitable where spread stationary process → cointegration unable to capture some behabiour like regime-switches → parametric models (Nelson-Siegel) c 2015 H¨aner Consulting CCR&CVA under Basel III 114 / 205
  115. 115. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development GBM with Term Structure Interpolation Principles Interpolate dimension-less quantities Forward Drift/Covariance Dimensionality analysis → interpolate TΩ c 2015 H¨aner Consulting CCR&CVA under Basel III 115 / 205
  116. 116. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Factor Models Issues with general covariance matrix N risk factors →∝ N2 parameters over-parametrization for empirical parameters: problems with positive definiteness Idea Split return r of riskfactors into contributions from Indices fn shared by multiple risk factors Idiosycratic factors unique to each risk factor r = α + n βnfn + and assume indices uncorrelated to indosyncraticsc 2015 H¨aner Consulting CCR&CVA under Basel III 116 / 205
  117. 117. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Types of Factor Models Classification Macroeconomic Observables like changes in inflation, interest rate, unemployment rate Fundamental Portfolios associated to security attributes like industry membership, book to market ratio, dividends Statistical Factor analysis of covariance matrix c 2015 H¨aner Consulting CCR&CVA under Basel III 117 / 205
  118. 118. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Macroeconomic Factor Model Fast/Slow Slow variables Macro-economic state of the economy: inflation, unemployment rate, GDP Fast Asset prices Pros and Cons ⊕ Designed to predict long-term evolution ⊕ Able to reflect systemic macro risks Empirical evidence not convincing Theories controversial c 2015 H¨aner Consulting CCR&CVA under Basel III 118 / 205
  119. 119. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Fundamental Factor Model Sector/Region 1 Define for each sector/region pair an index 2 Associate stock to sector/region 3 Regress stock return vs index return → α, β Example FactorModel.xls Pros and Cons ⊕ Designed to predict long-term evolution ⊕ Able to reflect systemic macro risks Empirical evidence not convincing Theories controversialc 2015 H¨aner Consulting CCR&CVA under Basel III 119 / 205
  120. 120. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Choice of Factors How to know whether factors appropriate? Analyze variance explained by factors c 2015 H¨aner Consulting CCR&CVA under Basel III 120 / 205
  121. 121. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Volatility Clustering : Spot : Log-returns Figure: GBPUSD spot c 2015 H¨aner Consulting CCR&CVA under Basel III 121 / 205
  122. 122. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Autocorrelation : Autocorrelation: log-returns : Autocorrelation: squaredc 2015 H¨aner Consulting CCR&CVA under Basel III 122 / 205
  123. 123. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Garch Model Let Xn be the log-return of some foreign exchange rate f at time tn: Xn = ln fn fn−1 (4) we may then express the foreign exchange rate fN at some future sampling point time tN by the initial value f0 at t0 and a series of returns: fN = f0e N i=1 Xi (5) The observation points ti are typically defined in terms of number of business days ∆T between them. For short time horizon predictions we choose ∆T = 1 for larger horizon, we may choose a less granular time grid. c 2015 H¨aner Consulting CCR&CVA under Basel III 123 / 205
  124. 124. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Garch Model The dynamics of the returns is then assumed to follow a Garch(1,1) process Xn = µ + n t ∼ iid(0, σ2 n) (6) σ2 n+1 = α + βσ2 n + γ 2 n (7) The asymptotic value σ2 ∞ = limn→∞ E[σ2 n] is then obtained by equation (7) noting, that E[ 2] = σ2 and E[σ2 n+1] → E[σ2 n]: σ∞ = α 1 − β − γ (8) c 2015 H¨aner Consulting CCR&CVA under Basel III 124 / 205
  125. 125. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Garch Model: Limit Weak limit: Stochastic variance Mean reverting variance dXt = µXtdt + √ vtXtdWt dvt = α(vt)dt + β(vt)dZt c 2015 H¨aner Consulting CCR&CVA under Basel III 125 / 205
  126. 126. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Copula Dependence under Stress In stressed markets correlations increase between downward price movements → systematic risk implied default probabilities → contagion Definition (Copula) Separate Marginal distributions from Dependency c 2015 H¨aner Consulting CCR&CVA under Basel III 126 / 205
  127. 127. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Cointegration Long-run Relationship Variables moving together: Macro-economic Consumption-Income Prices-Wages Domestic prices - fpreign prices Exogeneous For instance managed currencies How to model processes. which stay close to each other? GBM with ρij 1 not? No! Need dynamic, where difference is stationary Definition Stochastic processes x, y are cointegrated: y(t) = a + bx(t) + ξ(t)c 2015 H¨aner Consulting CCR&CVA under Basel III 127 / 205
  128. 128. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Implementation 1 find parameters a, b by regression 2 show residuals are stationary (e.g. Dickey-Fuller Test) Example Cointegration.xlsx c 2015 H¨aner Consulting CCR&CVA under Basel III 128 / 205
  129. 129. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Risk Factor Models Empirical Models Nelson-Siegel model r(T) = r∞ + a(T)r0 + b(T)rm r∞ : rate for long maturities r0 : rate for short maturities rm : rate for intermediate maturities a, b : decay functions c 2015 H¨aner Consulting CCR&CVA under Basel III 129 / 205
  130. 130. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Risk Factor Models Empirical Models Nelson-Siegel model Normal/inverted curves But not arbitrage-free How to introduce dynamics? E.g. PCA of (r∞, r0, rm) Example NelsonSiegel.xlsm c 2015 H¨aner Consulting CCR&CVA under Basel III 130 / 205
  131. 131. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Wrong Way Risk Types Specific Legal connection between underlying and counterparty General Dependence between prob. of default of counterparty and exposure SFT Transactions Lend cash to counterparty A accepting their stock as collateral. Emerging Market CCY swap We are long strong currency. Weakening of emerging market currency, increased prob default → increase exposure c 2015 H¨aner Consulting CCR&CVA under Basel III 131 / 205
  132. 132. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Modelling Wrong Way Risk What is wrong with standard modelling? p+ is not conditioned on default. Need to add in price function default state χ of counterparty: extending state of the world Approaches Given a model for default times either Simulating counterparty’s default Calculating price given default Example WrongWayRisk.xls c 2015 H¨aner Consulting CCR&CVA under Basel III 132 / 205
  133. 133. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Collateral Modeling Components Margin Call Process Model margin calls with correct frequency and close-out period Collateral Price E.g. model bond price if collateral is bond Simplification Margin call process: just at spot → short-cut method All collateral as cash → haircuts c 2015 H¨aner Consulting CCR&CVA under Basel III 133 / 205
  134. 134. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Collateral Modeling Short-Cut Method Definition (Basel II Short-Cut Method) EE and PE of collateralized trades given by EE and PE for close-out period (5 days for SFT, 10d for OTC) Benefits/Issues ⊕ Computationally cheap ⊕ No collateral exposure spikes at expity Assumes exposures declining over time Risk not accurately represented c 2015 H¨aner Consulting CCR&CVA under Basel III 134 / 205
  135. 135. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Dependency Modelling Among Risk Factors Standard way to model dependence: Gaussian Copula. Gaussian Copulas are Levy copulas. Replace Gaussian with other Levy coupula and obtain Levy model. Between Defaults Simulate either Default times τ E.g. by Marshall-Olkin Copulas Default state at t:χτ≤t E.g. structural models c 2015 H¨aner Consulting CCR&CVA under Basel III 135 / 205
  136. 136. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Dependency Modelling Between a Default and Risk Factors To caputure Wrong Way risk need to model dependence between risk factor and default state Example WrongWayRisk.xls Between a cross name Defaults and Risk Factors Need modelling full state of the world (x(t), {χτ1≤t, . . . χτ1≤t}). → scenario consistency is system c 2015 H¨aner Consulting CCR&CVA under Basel III 136 / 205
  137. 137. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Model Lifecycle Organisation Execution Problem Definition Analysis Implementation Test Deployment MaintananceChanges Figure: Model Development Lifcecyle c 2015 H¨aner Consulting CCR&CVA under Basel III 137 / 205
  138. 138. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Specification Approaches Human readable Business and functional specs Machine readable Specification ∼ test c 2015 H¨aner Consulting CCR&CVA under Basel III 138 / 205
  139. 139. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Specification Tools ScalaTest Code c 2015 H¨aner Consulting CCR&CVA under Basel III 139 / 205
  140. 140. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Specification Tools ScalaTest Output Part of CI: c 2015 H¨aner Consulting CCR&CVA under Basel III 140 / 205
  141. 141. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Implementation Software in-house third-party Require different validation strategies c 2015 H¨aner Consulting CCR&CVA under Basel III 141 / 205
  142. 142. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Third Party Strategies Black-box, no code review Reverse-engineering c 2015 H¨aner Consulting CCR&CVA under Basel III 142 / 205
  143. 143. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Revision Control Requirements Audit Who changed what/when Resurrect Roll-back to previous state Collaborate Merge contributions from different authors Approaches Plain files Tag files/directories with version information Local Local database contains version information (e.g RCS) Server Database on server (e.g. SVN) Distributed Each developer has own databse with potentially central db (e.g. Git) c 2015 H¨aner Consulting CCR&CVA under Basel III 143 / 205
  144. 144. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Revison Control Tools Approaches MyDirectoryV1.0 MyDirectoryV1.1 MyDirectoryV1.2-bugfix1 : File based : Local VCS c 2015 H¨aner Consulting CCR&CVA under Basel III 144 / 205
  145. 145. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Revison Control Tools Approaches : Centralized VCS : Distributed VCS c 2015 H¨aner Consulting CCR&CVA under Basel III 145 / 205
  146. 146. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Revision Control Tools Git Figure: Git Gui (SourceTree) c 2015 H¨aner Consulting CCR&CVA under Basel III 146 / 205
  147. 147. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Documentation Requirement Contain enough information to reverse-engineer. Tools Automated API doc (Doxygen, ScalaDoc, . . .) Internal wiki (e.g. Confluence) c 2015 H¨aner Consulting CCR&CVA under Basel III 147 / 205
  148. 148. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Testing Test Types Unit Library level Integration System level c 2015 H¨aner Consulting CCR&CVA under Basel III 148 / 205
  149. 149. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Testing Unit Test c 2015 H¨aner Consulting CCR&CVA under Basel III 149 / 205
  150. 150. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Release Requirements Regression Impact analysis Sign-off Auditing Lock-down c 2015 H¨aner Consulting CCR&CVA under Basel III 150 / 205
  151. 151. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Maintance Bugs/Enhanements Tracking system Failing test cases Metrics: severity, resolution time c 2015 H¨aner Consulting CCR&CVA under Basel III 151 / 205
  152. 152. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Analysis Models Software Development Integrated Development Process Robust system should have Components Revsion Control system Build System Bug tracking system Wikin Components integrated to workflow with high degree of automation c 2015 H¨aner Consulting CCR&CVA under Basel III 152 / 205
  153. 153. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Overview 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 153 / 205
  154. 154. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Motivation Impact of Credit risk model Trading activity limits set by PE Capital charges regularity capital dependent of EEPE P&L EE enters CVA/DVA Model Risk Back-testing should quantify model risk affecting these quantities. c 2015 H¨aner Consulting CCR&CVA under Basel III 154 / 205
  155. 155. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Requirements Back-testing Process Should provide Definition of measure for model risk Monitoring of metrics Mitigating actions for model deficiencies c 2015 H¨aner Consulting CCR&CVA under Basel III 155 / 205
  156. 156. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G1 G2 G3 c 2015 H¨aner Consulting CCR&CVA under Basel III 156 / 205
  157. 157. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G4 G5 G6 c 2015 H¨aner Consulting CCR&CVA under Basel III 157 / 205
  158. 158. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G7 G8 G9 c 2015 H¨aner Consulting CCR&CVA under Basel III 158 / 205
  159. 159. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G10 G11 G12 c 2015 H¨aner Consulting CCR&CVA under Basel III 159 / 205
  160. 160. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G13 G14 G15 c 2015 H¨aner Consulting CCR&CVA under Basel III 160 / 205
  161. 161. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance BCBS Guidance G16 c 2015 H¨aner Consulting CCR&CVA under Basel III 161 / 205
  162. 162. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance What is the Question? Types of Investigation Hypothesis testing (Answer in percentage or yes/no) Estimation of model uncertainty (Answer in cash terms) Analysis at different levels: figure 9 c 2015 H¨aner Consulting CCR&CVA under Basel III 162 / 205
  163. 163. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Domains Economic Quantities Regulatory Capital Limits CVA/DVA Risk Measures EEPE PE EE Process Characterictics Marginal Distributions Auto-Correlations N-Point Functions Model-Dependent Quantities Model Parameters Driver dynamic Figure: Domainsc 2015 H¨aner Consulting CCR&CVA under Basel III 163 / 205
  164. 164. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Definition A model is represented by a measure Q. May be generated by a stochastic process. Quantifying Difference of Models Comparing expectation values Comparing probability distributions Note: PDFs and CDFs may be expressed as expectation values c 2015 H¨aner Consulting CCR&CVA under Basel III 164 / 205
  165. 165. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Radon-Nikodym Derivative Distance of model Q and end empirical measure P in terms of dP dQ: EP[f ] = EQ[ dP dQ f ] (9) Compare P and Q Direct dP dQ ≈ id? Expectation values Empirical expectation measures in terms of model expectations Relative Entropy Kullback-Leibler entropy → information geometry (see [?]) c 2015 H¨aner Consulting CCR&CVA under Basel III 165 / 205
  166. 166. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Radon-Nikodym Derivative Let ξ be a scalar stochastic variable (e.g. portfolio price π(t)) Definition P empirical, Q model CDF Ψ : [0, 1] → [0, 1] (10) Ψ(α) = P(Q−1 (α)) (11) Radon-Nikodym derivative ψ EP[f ] = EQ[ψ(α)f ] (12) ψ(α) = dΨ(α) dα (13) c 2015 H¨aner Consulting CCR&CVA under Basel III 166 / 205
  167. 167. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Example : 0.0 0.2 0.4 0.6 0.8 1.0 α 0.0 0.2 0.4 0.6 0.8 1.0 Ψ(α) [x]=100.00;σ=0.40 [x]=110.00;σ=0.40 [x]=90.00;σ=0.40 [x]=100.00;σ=0.44 [x]=100.00;σ=0.36 0.8 1.0 1.2 1.4 1.6 1.8 ψ(α) [x]=100.00;σ=0.40 [x]=110.00;σ=0.40 [x]=90.00;σ=0.40 [x]=100.00;σ=0.44 [x]=100.00;σ=0.36 c 2015 H¨aner Consulting CCR&CVA under Basel III 167 / 205
  168. 168. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Cumulative Distribution Functions Cumulative distribution function (CDF) for some state variable ξ expressed as expectation: Definition P(ξ0) = EP[Θ(ξ − ξ0)] (14) where Θ is the Heaviside function. c 2015 H¨aner Consulting CCR&CVA under Basel III 168 / 205
  169. 169. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Estimating Ensemble averages E estimated well by time averages if ergodic stationary CDF P(ξ0) ≈ 1 N N i=1 Θ(ξ(ti ) − ξ0) (15) Ψ Ψ(α) ≈ 1 N N i=1 Θ(ξ(ti ) − Q−1 (α)) (16) c 2015 H¨aner Consulting CCR&CVA under Basel III 169 / 205
  170. 170. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Requirements for Estimation Process neeeds to be ergodic stationary iid price process If empirical price process is iid, the ergodic. iid process of underlying Even if underlying process the price return process of the deal may not be so, if deal not time homogeneus c 2015 H¨aner Consulting CCR&CVA under Basel III 170 / 205
  171. 171. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Distances Point Distance di = |Ψ(qi ) − qi | (17) Curve Distance (Weighted) quadratic distance d between functions q → Ψ(q) and q → q: d(q, Ψ(q)) = i wi (Ψ(qi ) − qi )2 (18) qi e.g (0.01, 0.05, 0.3, 0.5, 0.7, 0.95, 0.99) c 2015 H¨aner Consulting CCR&CVA under Basel III 171 / 205
  172. 172. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Hypothesis Testing Null-Hypothesis Null-Hypothesis, is that distances are 0. Reject Null-Hypothesis p-values smaller than some threshold Challenges estimating p-values Temporal dependence: overlap of time-windows Ensemble dependence: returns of netting sets not independent Good p values get bigger Bad Estimation tricky Need some simplifications, like effective sample sizes c 2015 H¨aner Consulting CCR&CVA under Basel III 172 / 205
  173. 173. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Problems using metrics for Ψ Issues using metrics for Ψ Opaque no cash denominated measure Economics Product Dependent with same distance different moments drive deviations in EE (see figure (11)) Limited usefulness Passes test if not enough data available c 2015 H¨aner Consulting CCR&CVA under Basel III 173 / 205
  174. 174. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Problems using metrics for Ψ 20 40 60 80 100 120 140 160 strike K 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 EE EE [x]=100.00;σ=0.40 [x]=110.00;σ=0.40 [x]=90.00;σ=0.40 [x]=100.00;σ=0.44 [x]=100.00;σ=0.36 Figure: Comparing EEs for a forward using log-normal distributions with different parameters c 2015 H¨aner Consulting CCR&CVA under Basel III 174 / 205
  175. 175. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulatory Requirements Measuring Model Performance Comparison using Cash denominated Quantities Economically Relevant Model Dependent Quantities Regulatory Capital depends on EE(t) (through EEPE) Limits impacted by CDF P&L impacted by EE(t) Measure These three quantities are functions of EQ. Their value under empirical measure P estimated through equation (12) → difference in cash terms c 2015 H¨aner Consulting CCR&CVA under Basel III 175 / 205
  176. 176. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Overview 1 Credit Risk Measures 2 Credit Risk Mitigation 3 Model Implementation 4 Back Testing 5 Regulatory Requirements and Basel III c 2015 H¨aner Consulting CCR&CVA under Basel III 176 / 205
  177. 177. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Pillars of Basel II Framework Minimum Capital Requirements Pillar I Credit Risk Market Risk Operational Risk Supervisory Review Process Pillar II Regulatory Framework Supervisory Framework Market Discipline Pillar III Disclosure Basel II Accord c 2015 H¨aner Consulting CCR&CVA under Basel III 177 / 205
  178. 178. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Basel II Capital Charges Based on Expected Exposures (EE) of netting sets Charge for default risk No charge for credit spread risk c 2015 H¨aner Consulting CCR&CVA under Basel III 178 / 205
  179. 179. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III New in Basel III In 2008 crisis: 2 3 of losses not due to default but MtM changes due to credit spread widening Capture spread risk by VaR Introduction of new capital charge linked to VaR: CVA charge Capital Charges Basel II Default charges Basel III Default and CVA charges c 2015 H¨aner Consulting CCR&CVA under Basel III 179 / 205
  180. 180. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III CVA charge Advanced CVA Charge VaR for credit spread for bond given by EE: c 2015 H¨aner Consulting CCR&CVA under Basel III 180 / 205
  181. 181. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III CVA charge Standardised CVA Charge c 2015 H¨aner Consulting CCR&CVA under Basel III 181 / 205
  182. 182. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III CVA charge Advanced vs Standardised Advanced Standardized Reflect Diversification ⊕ Accurate Credit Spreads ⊕ Regulatory Capital ⊕ Build/Approval Costs ⊕ Running Costs ⊕ Synergies with Market Risk ⊕ Integration with CVA desk ⊕ c 2015 H¨aner Consulting CCR&CVA under Basel III 182 / 205
  183. 183. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III IMM Internal Model Method Institutions who have IMM waiver may calculate their own regulatory capital for OTC transactions Swaps, exotic deals, . . . SFT transactions Bond repos, stock borrow/lending, . . . c 2015 H¨aner Consulting CCR&CVA under Basel III 183 / 205
  184. 184. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III IMM Benefits Reduced capital charges More accurate risk measures Consistent risk measures for Regualtory capital Limit monitoring Improved Processes Quality of information c 2015 H¨aner Consulting CCR&CVA under Basel III 184 / 205
  185. 185. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Wrong Way Risk Specific Wrong Way Risk c 2015 H¨aner Consulting CCR&CVA under Basel III 185 / 205
  186. 186. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Wrong Way Risk Stressed Calibration c 2015 H¨aner Consulting CCR&CVA under Basel III 186 / 205
  187. 187. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Stressed Calibration Frquency of Comparison c 2015 H¨aner Consulting CCR&CVA under Basel III 187 / 205
  188. 188. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Hedges CVA Charges c 2015 H¨aner Consulting CCR&CVA under Basel III 188 / 205
  189. 189. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Hedges Default Charges c 2015 H¨aner Consulting CCR&CVA under Basel III 189 / 205
  190. 190. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Collateral Non Cash Collateral for OTC c 2015 H¨aner Consulting CCR&CVA under Basel III 190 / 205
  191. 191. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Other Proxy,Index Hedges c 2015 H¨aner Consulting CCR&CVA under Basel III 191 / 205
  192. 192. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Elements of Application A High-level overview and implementation plans B Overview of your firm’s own self assessment against relevant standards C Summary of your firm’s approach in a number of key areas D Details of the IMM models being used E Sign-off c 2015 H¨aner Consulting CCR&CVA under Basel III 192 / 205
  193. 193. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Overview/Implementation Plan Impact Analysis Scope Rollout Plan Orgchart c 2015 H¨aner Consulting CCR&CVA under Basel III 193 / 205
  194. 194. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Self Assessment Description of self sssessment process Results: exceptions, remediation plan and status c 2015 H¨aner Consulting CCR&CVA under Basel III 194 / 205
  195. 195. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Firm’s Approach Governance of Counterparty Risk Roles of senior management, risk functions, audit functions, legal functions, collateral management functions, and the functions of any committees Governance of the model, covering the organisation charts and reporting lines of the model owner, developers, and other support functions; an overview of the management committee structure which approved the model and; how external vendor models, if any, are controlled; ad-hoc and on going stress testing. c 2015 H¨aner Consulting CCR&CVA under Basel III 195 / 205
  196. 196. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Firm’s Approach Requirement for use of IMM Show methodology used for the calculation of the IMM exposure is closely integrated into its day-to-day risk management processes. Management information where the IMM generated exposure and any other outputs from the methodology is presented Management information used by senior management to monitor and control counterparty and market risk including the composition / profile of the portfolios, concentration risk, wrong way risk and the results of stress testing c 2015 H¨aner Consulting CCR&CVA under Basel III 196 / 205
  197. 197. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Firm’s Approach Data Management and Integrity Standards of data management; data architecture Process to ensure the accuracy, completeness and appropriateness Timeliness and robustness of the production systems Reconciliation finance and risk systems Business continuity c 2015 H¨aner Consulting CCR&CVA under Basel III 197 / 205
  198. 198. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Firm’s Approach Validation Accountability, independence, scope, documentation and monitoring the effectiveness of the model on an ongoing basis Explanation of how senior management obtain comfort that the outputs from the IMM model are sufficiently robust for the business Summary of your approach to back testing, including the methodology and assessment of the results c 2015 H¨aner Consulting CCR&CVA under Basel III 198 / 205
  199. 199. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Firm’s Approach Documentation List of all the internal documents you hold that you consider relevant to the application, including a brief description of their contents. Relevant documentation would cover documentation specific to the IMM as well as the controls surrounding it c 2015 H¨aner Consulting CCR&CVA under Basel III 199 / 205
  200. 200. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Details of the IMM models being used A description of the model coverage, in terms of businesses units, products and risk factors Documents relevant to the IMM, with dates when last updated. Including any pre-processing performed on transaction level information, features of the model, assumptions used, use of proxies, approximations, limitations of the output, modelling of risk factors, modelling of collateral and netting and, treatment of margins Use of market data Valuation analytics including assessment of how assumptions and approximations impact accuracy of the models c 2015 H¨aner Consulting CCR&CVA under Basel III 200 / 205
  201. 201. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Details of the IMM models being used Assessment of the model’s fitness for purpose in the light of the risks presented by the portfolio (e.g. correlation between counterparties’ exposures, wrong way risk) Analysis performed on an ad hoc or on going basis to monitor model performance Materiality, of any relevant risk factors not covered by the IMM Validation reports Enhancement plans c 2015 H¨aner Consulting CCR&CVA under Basel III 201 / 205
  202. 202. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III Beyond Basel III: FRTB Fundametal Review of the Trading Book (FRTB) BCBS proposals for next next generation Market Risk Framework (”Basel IV”): Fundamental review of the trading book: A revised Market Risk Framework, BCBS October 2014 Consultative Document Review of the Credit Valuation Adjustment Risk Framework, BCBS July 2015 c 2015 H¨aner Consulting CCR&CVA under Basel III 202 / 205
  203. 203. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III FRTB Proposals Boundary between banking and trading book (→ capital arbitrage) Improved granularity of Standardized Risk Charge Disclosure of Standardized Risk Charge c 2015 H¨aner Consulting CCR&CVA under Basel III 203 / 205
  204. 204. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III FRTB Proposals: Internal Model Approach Expected Shortfall (ES) replaces VaR; liquidity horizons ) Incremental Default Risk (IDR): jump to default of bond and equity positions Modellable/non-modellable risk factors Capital add-on from stress-testing for non-modellable risk factors c 2015 H¨aner Consulting CCR&CVA under Basel III 204 / 205
  205. 205. Credit Risk Measures Credit Risk Mitigation Model Implementation Back Testing Regulatory Requirements and Basel III Regulation IMM Waiver Application Beyond Basel III FRTB Proposals: FRTB-CVA Goal: make CVA charge consistent with FRTB Market Risk Framework: IMM-CVA → FRTB-CVA: Expected Shorfall instead of VaR Allow accounting CVA Sensivity of CVA wrt all risk factors instead of just spread CVA desk required c 2015 H¨aner Consulting CCR&CVA under Basel III 205 / 205

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