Counterparty Credit Risk, Collateral and Funding -- Contents -- Ignition -- Abbreviations and Notation -- PART I COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING -- 1 Introduction -- 1.1 A Dialogue on CVA -- 1.2 Risk Measurement: Credit VaR -- 1.3 Exposure, CE, PFE, EPE, EE, EAD -- 1.4 Exposure and Credit VaR -- 1.5 Interlude: P and Q -- 1.6 Basel -- 1.7 CVA and Model Dependence -- 1.8 Input and Data Issues on CVA -- 1.9 Emerging Asset Classes: Longevity Risk -- 1.10 CVA and Wrong Way Risk -- 1.11 Basel III: VaR of CVA and Wrong Way Risk -- 1.12 Discrepancies in CVA Valuation: Model Risk and Payoff Risk -- 1.13 Bilateral Counterparty Risk: CVA and DVA -- 1.14 First-to-Default in CVA and DVA -- 1.15 DVA Mark-to-Market and DVA Hedging -- 1.16 Impact of Close-Out in CVA and DVA -- 1.17 Close-Out Contagion -- 1.18 Collateral Modelling in CVA and DVA -- 1.19 Re-Hypothecation -- 1.20 Netting -- 1.21 Funding -- 1.22 Hedging Counterparty Risk: CCDS -- 1.23 Restructuring Counterparty Risk: CVA-CDOs and Margin Lending -- 2 Context -- 2.1 Definition of Default: Six Basic Cases -- 2.2 Definition of Exposures -- 2.3 Definition of Credit Valuation Adjustment (CVA) -- 2.4 Counterparty Risk Mitigants: Netting -- 2.5 Counterparty Risk Mitigants: Collateral -- 2.5.1 The Credit Support Annex (CSA) -- 2.5.2 The ISDA Proposal for a New Standard CSA -- 2.5.3 Collateral Effectiveness as a Mitigant -- 2.6 Funding -- 2.6.1 A First Attack on Funding Cost Modelling -- 2.6.2 The General Funding Theory and its Recursive Nature -- 2.7 Value at Risk (VaR) and Expected Shortfall (ES) of CVA -- 2.8 The Dilemma of Regulators and Basel III -- 3 Modelling the Counterparty Default -- 3.1 Firm Value (or Structural) Models -- 3.1.1 The Geometric Brownian Assumption -- 3.1.2 Merton's Model -- 3.1.3 Black and Cox's (1976) Model -- 3.1.4 Credit Default Swaps and Default Probabilities.

3.1.5 Black and Cox (B&C) Model Calibration to CDS: Problems -- 3.1.6 The AT1P Model -- 3.1.7 A Case Study with AT1P: Lehman Brothers Default History -- 3.1.8 Comments -- 3.1.9 SBTV Model -- 3.1.10 A Case Study with SBTV: Lehman Brothers Default History -- 3.1.11 Comments -- 3.2 Firm Value Models: Hints at the Multiname Picture -- 3.3 Reduced Form (Intensity) Models -- 3.3.1 CDS Calibration and Intensity Models -- 3.3.2 A Simpler Formula for Calibrating Intensity to a Single CDS -- 3.3.3 Stochastic Intensity: The CIR Family -- 3.3.4 The Cox-Ingersoll-Ross Model (CIR) Short-Rate Model for r -- 3.3.5 Time-Inhomogeneous Case: CIR++ Model -- 3.3.6 Stochastic Diffusion Intensity is Not Enough: Adding Jumps. The JCIR(++) Model -- 3.3.7 The Jump-Diffusion CIR Model (JCIR) -- 3.3.8 Market Incompleteness and Default Unpredictability -- 3.3.9 Further Models -- 3.4 Intensity Models: The Multiname Picture -- 3.4.1 Choice of Variables for the Dependence Structure -- 3.4.2 Firm Value Models? -- 3.4.3 Copula Functions -- 3.4.4 Copula Calibration, CDOs and Criticism of Copula Functions -- PART II PRICING COUNTERPARTY RISK: UNILATERAL CVA -- 4 Unilateral CVA and Netting for Interest Rate Products -- 4.1 First Steps towards a CVA Pricing Formula -- 4.1.1 Symmetry versus Asymmetry -- 4.1.2 Modelling the Counterparty Default Process -- 4.2 The Probabilistic Framework -- 4.3 The General Pricing Formula for Unilateral Counterparty Risk -- 4.4 Interest Rate Swap (IRS) Portfolios -- 4.4.1 Counterparty Risk in Single IRS -- 4.4.2 Counterparty Risk in an IRS Portfolio with Netting -- 4.4.3 The Drift Freezing Approximation -- 4.4.4 The Three-Moments Matching Technique -- 4.5 Numerical Tests -- 4.5.1 Case A: IRS with Co-Terminal Payment Dates -- 4.5.2 Case B: IRS with Co-Starting Resetting Date -- 4.5.3 Case C: IRS with First Positive, Then Negative Flow.

4.5.4 Case D: IRS with First Negative, Then Positive Flows -- 4.5.5 Case E: IRS with First Alternate Flows -- 4.6 Conclusions -- 5 Wrong Way Risk (WWR) for Interest Rates -- 5.1 Modelling Assumptions -- 5.1.1 G2++ Interest Rate Model -- 5.1.2 CIR++ Stochastic Intensity Model -- 5.1.3 CIR++ Model: CDS Calibration -- 5.1.4 Interest Rate/Credit Spread Correlation -- 5.1.5 Adding Jumps to the Credit Spread -- 5.2 Numerical Methods -- 5.2.1 Discretization Scheme -- 5.2.2 Simulating Intensity Jumps -- 5.2.3 "American Monte Carlo" (Pallavicini 2006) -- 5.2.4 Callable Payoffs -- 5.3 Results and Discussion -- 5.3.1 WWR in Single IRS -- 5.3.2 WWR in an IRS Portfolio with Netting -- 5.3.3 WWR in European Swaptions -- 5.3.4 WWR in Bermudan Swaptions -- 5.3.5 WWR in CMS Spread Options -- 5.4 Contingent CDS (CCDS) -- 5.5 Results Interpretation and Conclusions -- 6 Unilateral CVA for Commodities with WWR -- 6.1 Oil Swaps and Counterparty Risk -- 6.2 Modelling Assumptions -- 6.2.1 Commodity Model -- 6.2.2 CIR++ Stochastic-Intensity Model -- 6.3 Forward versus Futures Prices -- 6.3.1 CVA for Commodity Forwards without WWR -- 6.3.2 CVA for Commodity Forwards with WWR -- 6.4 Swaps and Counterparty Risk -- 6.5 UCVA for Commodity Swaps -- 6.5.1 Counterparty Risk from the Payer's Perspective: The Airline Computes Counterparty Risk -- 6.5.2 Counterparty Risk from the Receiver's Perspective: The Bank Computes Counterparty Risk -- 6.6 Inadequacy of Basel's WWR Multipliers -- 6.7 Conclusions -- 7 Unilateral CVA for Credit with WWR -- 7.1 Introduction to CDSs with Counterparty Risk -- 7.1.1 The Structure of the Chapter -- 7.2 Modelling Assumptions -- 7.2.1 CIR++ Stochastic-Intensity Model -- 7.2.2 CIR++ Model: CDS Calibration -- 7.3 CDS Options Embedded in CVA Pricing -- 7.4 UCVA for Credit Default Swaps: A Case Study -- 7.4.1 Changing the Copula Parameters.

7.4.2 Changing the Market Parameters -- 7.5 Conclusions -- 8 Unilateral CVA for Equity with WWR -- 8.1 Counterparty Risk for Equity Without a Full Hybrid Model -- 8.1.1 Calibrating AT1P to the Counterparty's CDS Data -- 8.1.2 Counterparty Risk in Equity Return Swaps (ERS) -- 8.2 Counterparty Risk with a Hybrid Credit-Equity Structural Model -- 8.2.1 The Credit Model -- 8.2.2 The Equity Model -- 8.2.3 From Barrier Options to Equity Pricing -- 8.2.4 Equity and Equity Options -- 8.3 Model Calibration and Empirical Results -- 8.3.1 BP and FIAT in 2009 -- 8.3.2 Uncertainty in Market Expectations -- 8.3.3 Further Results: FIAT in 2008 and BP in 2010 -- 8.4 Counterparty Risk and Wrong Way Risk -- 8.4.1 Deterministic Default Barrier -- 8.4.2 Uncertainty on the Default Barrier -- 9 Unilateral CVA for FX -- 9.1 Pricing with Two Currencies: Foundations -- 9.2 Unilateral CVA for a Fixed-Fixed CCS -- 9.2.1 Approximating the Volatility of Cross Currency Swap Rates -- 9.2.2 Parameterization of the FX Correlation -- 9.3 Unilateral CVA for Cross Currency Swaps with Floating Legs -- 9.4 Why a Cross Currency Basis? -- 9.4.1 The Approach of Fujii, Shimada and Takahashi (2010) -- 9.4.2 Collateral Rates versus Risk-Free Rates -- 9.4.3 Consequences of Perfect Collateralization -- 9.5 CVA for CCS in Practice -- 9.5.1 Changing the CCS Moneyness -- 9.5.2 Changing the Volatility -- 9.5.3 Changing the FX Correlations -- 9.6 Novations and the Cost of Liquidity -- 9.6.1 A Synthetic Contingent CDS: The Novation -- 9.6.2 Extending the Approach to the Valuation of Liquidity -- 9.7 Conclusions -- PART III ADVANCED CREDIT AND FUNDING RISK PRICING -- 10 New Generation Counterparty and Funding Risk Pricing -- 10.1 Introducing the Advanced Part of the Book -- 10.2 What We Have Seen Before: Unilateral CVA -- 10.2.1 Approximation: Default Bucketing and Independence.

10.3 Unilateral Debit Valuation Adjustment (UDVA) -- 10.4 Bilateral Risk and DVA -- 10.5 Undesirable Features of DVA -- 10.5.1 Profiting From Own Deteriorating Credit Quality -- 10.5.2 DVA Hedging? -- 10.5.3 DVA: Accounting versus Capital Requirements -- 10.5.4 DVA: Summary and Debate on Realism -- 10.6 Close-Out: Risk-Free or Replacement? -- 10.7 Can We Neglect the First-to-Default Time? -- 10.7.1 A Simplified Formula without First-to-Default: The Case of an Equity Forward -- 10.8 Payoff Risk -- 10.9 Collateralization, Gap Risk and Re-Hypothecation -- 10.10 Funding Costs -- 10.11 Restructuring Counterparty Risk -- 10.11.1 CVA Volatility: The Wrong Way -- 10.11.2 Floating Margin Lending -- 10.11.3 Global Valuation -- 10.12 Conclusions -- 11 A First Attack on Funding Cost Modelling -- 11.1 The Problem -- 11.2 A Closer Look at Funding and Discounting -- 11.3 The Approach Proposed by Morini and Prampolini (2010) -- 11.3.1 The Borrower's Case -- 11.3.2 The Lender's Case -- 11.3.3 The Controversial Role of DVA: The Borrower -- 11.3.4 The Controversial Role of DVA: The Lender -- 11.3.5 Discussion -- 11.4 What Next on Funding? -- 12 Bilateral CVA-DVA and Interest Rate Products -- 12.1 Arbitrage-Free Valuation of Bilateral Counterparty Risk -- 12.1.1 Symmetry versus Asymmetry -- 12.1.2 Worsening of Credit Quality and Positive Mark-to-Market -- 12.2 Modelling Assumptions -- 12.2.1 G2++ Interest Rate Model -- 12.2.2 CIR++ Stochastic Intensity Model -- 12.2.3 Realistic Market Data Set for CDS Options -- 12.3 Numerical Methods -- 12.4 Results and Discussion -- 12.4.1 Bilateral VA in Single IRS -- 12.4.2 Bilateral VA in an IRS Portfolio with Netting -- 12.4.3 Bilateral VA in Exotic Interest Rate Products -- 12.5 Conclusions -- 13 Collateral, Netting, Close-Out and Re-Hypothecation -- 13.1 Trading Under the ISDA Master Agreement.

13.1.1 Mathematical Setup and CBVA Definition.