XVA: Credit, Funding and Capital Valuation Adjustments -- Contents -- List of Tables -- List of Figures -- Acknowledgements -- Chapter 1 Introduction: The Valuation of Derivative Portfolios -- 1.1 What this book is about -- 1.2 Prices and Values -- 1.2.1 Before the Fall... -- 1.2.2 The Post-Crisis World... -- 1.3 Trade Economics in Derivative Pricing -- 1.3.1 The Components of a Price -- 1.3.2 Risk-Neutral Valuation -- 1.3.3 Hedging and Management Costs -- 1.3.4 Credit Risk: CVA/DVA -- 1.3.5 FVA -- 1.3.6 Regulatory Capital and KVA -- 1.4 Post-Crisis Derivative Valuation or How I Learned to Stop Worrying and Love FVA -- 1.4.1 The FVA Debate and the Assault on Black-Scholes-Merton -- 1.4.2 Different Values for Different Purposes -- 1.4.3 Summary: The Valuation Paradigm Shift -- 1.5 Reading this Book -- Part 1 CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment -- Chapter 2 Introducing Counterparty Risk -- 2.1 Defining Counterparty Risk -- 2.1.1 Wrong-way and Right-way Risk -- 2.2 CVA and DVA: Credit Valuation Adjustment and Debit Valuation Adjustment Defined -- 2.3 The Default Process -- 2.3.1 Example Default: The Collapse of Lehman Brothers -- 2.4 Credit Risk Mitigants -- 2.4.1 Netting -- 2.4.2 Collateral/Security -- 2.4.3 Central Clearing and Margin -- 2.4.4 Capital -- 2.4.5 Break Clauses -- 2.4.6 Buying Protection -- Chapter 3 CVA and DVA: Credit and Debit Valuation Adjustment Models -- 3.1 Introduction -- 3.1.1 Close-out and CVA -- 3.2 Unilateral CVA Model -- 3.2.1 Unilateral CVA by Expectation -- 3.2.2 Unilateral CVA by Replication -- 3.3 Bilateral CVA Model: CVA and DVA -- 3.3.1 Bilateral CVA by Expectation -- 3.3.2 Bilateral CVA by Replication -- 3.3.3 DVA and Controversy -- 3.4 Modelling Dependence between Counterparties -- 3.4.1 Gaussian Copula Model -- 3.4.2 Other Copula Models.

3.5 Components of a CVA Calculation Engine -- 3.5.1 Monte Carlo Simulation -- 3.5.2 Trade Valuation and Approximations -- 3.5.3 Expected Exposure Calculation -- 3.5.4 Credit Integration -- 3.6 Counterparty Level CVA vs. Trade Level CVA -- 3.6.1 Incremental CVA -- 3.6.2 Allocated CVA -- 3.7 Recovery Rate/Loss-Given-Default Assumptions -- Chapter 4 CDS and Default Probabilities -- 4.1 Survival Probabilities and CVA -- 4.2 Historical versus Implied Survival Probabilities -- 4.3 Credit Default Swap Valuation -- 4.3.1 Credit Default Swaps -- 4.3.2 Premium Leg -- 4.3.3 Protection Leg -- 4.3.4 CDS Value and Breakeven Spread -- 4.4 Bootstrapping the Survival Probability Function -- 4.4.1 Upfront Payments -- 4.4.2 Choice of Hazard Rate Function and CVA: CVA Carry -- 4.4.3 Calibration Problems -- 4.5 CDS and Capital Relief -- 4.6 Liquid and Illiquid Counterparties -- 4.6.1 Mapping to Representative CDS -- 4.6.2 Mapping to Baskets and Indices -- 4.6.3 Cross-sectional Maps -- Chapter 5 Analytic Models for CVA and DVA -- 5.1 Analytic CVA Formulae -- 5.2 Interest Rate Swaps -- 5.2.1 Unilateral CVA -- 5.2.2 Bilateral CVA -- 5.3 Options: Interest Rate Caplets and Floorlets -- 5.4 FX Forwards -- Chapter 6 Modelling Credit Mitigants -- 6.1 Credit Mitigants -- 6.2 Close-out Netting -- 6.3 Break Clauses -- 6.3.1 Mandatory Break Clauses -- 6.3.2 Optional Break Clauses -- 6.4 Variation Margin and CSA Agreements -- 6.4.1 Simple Model: Modifying the Payout Function -- 6.4.2 Modelling Collateral Directly -- 6.4.3 Lookback Method -- 6.4.4 Modelling Downgrade Triggers in CSA Agreements -- 6.5 Non-financial Security and the Default Waterfall -- Chapter 7 Wrong-way and Right-way Risk for CVA -- 7.1 Introduction: Wrong-way and Right-way Risks -- 7.1.1 Modelling Wrong-way Risk and CVA -- 7.2 Distributional Models of Wrong-way/Right-way Risk.

7.2.1 Simple Model: Increased Exposure -- 7.2.2 Copula Models -- 7.2.3 Linear Models and Discrete Models -- 7.3 A Generalised Discrete Approach to Wrong-Way Risk -- 7.4 Stochastic Credit Models of Wrong-way/Right-way Risk -- 7.4.1 Sovereign Wrong-way Risk -- 7.5 Wrong-way/Right-way Risk and DVA -- Part 2 FVA: Funding Valuation Adjustment -- Chapter 8 The Discount Curve -- 8.1 Introduction -- 8.2 A Single Curve World -- 8.3 Curve Interpolation and Smooth Curves -- 8.4 Cross-currency Basis -- 8.5 Multi-curve and Tenor Basis -- 8.6 OIS and CSA Discounting -- 8.6.1 OIS as the Risk-free Rate -- 8.6.2 OIS and CSA Discounting -- 8.6.3 Multi-currency Collateral and the Collateral Option -- 8.7 Conclusions: Discounting -- Chapter 9 Funding Costs: Funding Valuation Adjustment (FVA) -- 9.1 Explaining Funding Costs -- 9.1.1 What is FVA? -- 9.1.2 General Principle of Funding Costs -- 9.2 First Generation FVA: Discount Models -- 9.3 Double Counting and DVA -- 9.4 Second Generation FVA: Exposure Models -- 9.4.1 The Burgard-Kjaer Semi-Replication Model -- 9.5 Residual FVA and CSAs -- 9.6 Asymmetry -- 9.6.1 Case 1: Corporate vs. Bank Asymmetry -- 9.6.2 Case 2: Bank vs. Bank Asymmetry -- 9.7 Risk Neutrality, Capital and the Modigliani-Miller Theorem -- 9.7.1 No Market-wide Risk-neutral Measure -- 9.7.2 Consequences -- 9.7.3 The Modigliani-Miller Theorem -- 9.8 Wrong-way/Right-way Risk and FVA -- Chapter 10 Other Sources of Funding Costs: CCPs and MVA -- 10.1 Other Sources of Funding Costs -- 10.1.1 Central Counterparty Funding Costs -- 10.1.2 Bilateral Initial Margin -- 10.1.3 Rating Agency Volatility Buffers and Overcollateralisation -- 10.1.4 Liquidity Buffers -- 10.2 MVA: Margin Valuation Adjustment by Replication -- 10.2.1 Semi-replication with no Shortfall on Default -- 10.3 Calculating MVA Efficiently -- 10.3.1 Sizing the Problem.

10.3.2 Aside: Longstaff-Schwartz for Valuations and Expected Exposures -- 10.3.3 Calculating VaR inside a Monte Carlo -- 10.3.4 Case Study: Swap Portfolios -- 10.3.5 Adapting LSAC to VaR under Delta-Gamma Approximation -- 10.4 Conclusions on MVA -- Chapter 11 The Funding Curve -- 11.1 Sources for the Funding Curve -- 11.1.1 Term Funding -- 11.1.2 Rolling Funding -- 11.2 Internal Funding Curves -- 11.2.1 Bank CDS Spread -- 11.2.2 Bank Bond Spread -- 11.2.3 Bank Bond-CDS Basis -- 11.2.4 Bank Treasury Transfer Price -- 11.2.5 Funding Strategy Approaches -- 11.3 External Funding Curves and Accounting -- 11.4 Multi-currency/Multi-asset Funding -- Part 3 KVA: Capital Valuation Adjustment and Regulation -- Chapter 12 Regulation: the Basel II and Basel III Frameworks -- 12.1 Introducing the Regulatory Capital Framework -- 12.1.1 Economic Capital -- 12.1.2 The Development of the Basel Framework -- 12.1.3 Pillar I: Capital Types and Choices -- 12.2 Market Risk -- 12.2.1 Trading Book and Banking Book -- 12.2.2 Standardised Method -- 12.2.3 Internal Model Method (IMM) -- 12.3 Counterparty Credit Risk -- 12.3.1 Weight Calculation -- 12.3.2 EAD Calculation -- 12.3.3 Internal Model Method (IMM) -- 12.4 CVA Capital -- 12.4.1 Standardised -- 12.4.2 Advanced -- 12.5 Other Sources of Regulatory Capital -- 12.5.1 Incremental Risk Charge (IRC) -- 12.5.2 Leverage Ratio -- 12.6 Forthcoming Regulation with Pricing Impact -- 12.6.1 Fundamental Review of the Trading Book -- 12.6.2 Revised Standardised Approach to Credit Risk -- 12.6.3 Bilateral Initial Margin -- 12.6.4 Prudent Valuation -- 12.6.5 EMIR and Frontloading -- Chapter 13 KVA: Capital Valuation Adjustment -- 13.1 Introduction: Capital Costs in Pricing -- 13.1.1 Capital, Funding and Default -- 13.2 Extending Semi-replication to Include Capital -- 13.3 The Cost of Capital.

13.4 KVA for Market Risk, Counterparty Credit Risk and CVA Regulatory Capital -- 13.4.1 Standardised Approaches -- 13.4.2 IMM Approaches -- 13.5 The Size of KVA -- 13.6 Conclusion: KVA -- Chapter 14 CVA Risk Warehousing and Tax Valuation Adjustment (TVA) -- 14.1 Risk Warehousing XVA -- 14.2 Taxation -- 14.3 CVA Hedging and Regulatory Capital -- 14.4 Warehousing CVA Risk and Double Semi-Replication -- Chapter 15 Portfolio KVA and the Leverage Ratio -- 15.1 The Need for a Portfolio Level Model -- 15.2 Portfolio Level Semi-replication -- 15.3 Capital Allocation -- 15.3.1 Market Risk -- 15.3.2 Counterparty Credit Risk (CCR) -- 15.3.3 CVA Capital -- 15.3.4 Leverage Ratio -- 15.3.5 Capital Allocation and Uniqueness -- 15.4 Cost of Capital to the Business -- 15.5 Portfolio KVA -- 15.6 Calculating Portfolio KVA by Regression -- Part 4 XVA Implementation -- Chapter 16 Hybrid Monte Carlo Models for XVA: Building a Model for the Expected-Exposure Engine -- 16.1 Introduction -- 16.1.1 Implementing XVA -- 16.1.2 XVA and Monte Carlo -- 16.1.3 XVA and Models -- 16.1.4 A Roadmap to XVA Hybrid Monte Carlo -- 16.2 Choosing the Calibration: Historical versus Implied -- 16.2.1 The Case for Historical Calibration -- 16.2.2 The Case for Market Implied Calibration -- 16.3 The Choice of Interest Rate Modelling Framework -- 16.3.1 Interest Rate Models (for XVA) -- 16.3.2 The Heath-Jarrow-Morton (HJM) Framework and Models of the Short Rate -- 16.3.3 The Brace-Gaterak-Musiela (BGM) or Market Model Framework -- 16.3.4 Choice of Numeraire -- 16.3.5 Multi-curve: Tenor and Cross-currency Basis -- 16.3.6 Close-out and the Choice of Discount Curve -- 16.4 FX and Cross-currency Models -- 16.4.1 A Multi-currency Generalised Hull-White Model -- 16.4.2 The Triangle Rule and Options on the FX Cross -- 16.4.3 Models with FX Volatility Smiles -- 16.5 Inflation.

16.5.1 The Jarrow-Yildirim Model (using Hull-White Dynamics).