The xVA Challenge

The definitive guide to counterparty risk and valuation adjustments, updated and revised In the newly revised fifth edition of The xVA Challenge, veteran quantitative finance and counterparty credit risk expert Jon Gregory delivers an authoritative roadmap to navigating counterparty risk, funding, collateral, capital, and initial margin. He draws on his extensive experience as a former senior practitioner at Barclays Capital, BNP Paribas, and Citigroup to walk you through the most urgent challenges facing risk managers, traders, and derivatives practitioners right now. The book explores the latest developments in xVA methodology and practice, guiding you through advanced compression tools for counterparty risk optimisation, detailed ColVA analysis with real-world examples, and the evolving mandate of xVA desks in volatile market conditions. It examines FRTB-CVA implementation challenges, current approaches to KVA and MVA in banking operations, and cutting-edge machine learning and algorithmic differentiation techniques. You’ll also find: Comprehensive coverage of all xVA components including CVA, DVA, FVA, ColVA, KVA, and MVA with practical implementation guidance Detailed analyses of FRTB-CVA regulatory requirements and SA-CVA model development for regulatory approval Advanced compression techniques and optimization strategies for managing counterparty risk and xVA exposure Real-world case studies and examples demonstrating ColVA applications and xVA desk operations during market volatility State-of-the-art computational methods including machine learning approaches and algorithmic differentiation for enhanced calculation efficiency Perfect for risk managers, traders, derivatives practitioners, and financial regulators, The xVA Challenge, Fifth Edition, offers essential updates and practical tools that contemporary finance professionals need to effectively implement xVA frameworks, optimise counterparty risk management, and navigate an increasingly fraught regulatory landscape.

List of Spreadsheets xix List of Appendices xxi Acknowledgements xxiii About the Author xxv Part I Background 1 Introduction 3 2 Derivatives 5 2.1 Introduction 5 2.2 The Derivatives Market 7 2.3 Derivative Risks 19 2.4 Central Clearing 24 2.5 Derivatives Risk Modelling 29 3 Counterparty Risk and xVA 35 3.1 Counterparty Risk 35 3.2 Beyond Counterparty Risk 48 3.3 Components of xVA 51 4 Regulation 57 4.1 Capital Requirements 58 4.2 Backstops and Complementary Measures 65 4.3 Liquidity 68 4.4 Clearing and Margining 74 5 What Is xVA? 81 5.1 Overview 81 5.2 Anatomy of xVA 82 5.3 Valuation 91 5.4 Pricing 100 Part II Counterparty Risk Mitigation 6 Netting, Close-Out and Related Aspects 113 6.1 Overview 113 6.2 Cash Flow Netting 114 6.3 Netting in Default 123 7 Collateral, Margin and Settlement 133 7.1 Termination and Reset Features 133 7.2 Basics of Collateralisation 137 7.3 Collateral Terms 144 7.4 Standard CSAs 154 7.5 Impact of Collateral 159 8 Central Clearing 167 8.1 Evolution of Central Clearing 167 8.2 CCP Risk Management 178 8.3 Impact of Central Clearing 185 9 Initial Margin Methodologies 191 9.1 Overview 191 9.2 SPAN 200 9.3 Historical Simulation 206 9.4 Bilateral Initial Margin and the ISDA-SIMM 218 Part III Building Blocks 10 Future Value and Exposure 235 10.1 Credit Exposure 235 10.2 Drivers of Exposure 243 10.3 Portfolio Effects and the Impact of Collateral 253 10.4 Funding, Rehypothecation and Segregation 265 11 Curves 273 11.1 Default Probability 273 11.2 Credit Curve Mapping 280 11.3 Funding and Capital 291 12 Regulatory Methodologies 307 12.1 Overview 307 12.2 Credit Risk (Default Risk) Capital 310 12.3 CVA Risk 312 12.4 Exposure Calculation Methodologies 322 12.5 Examples 337 12.6 CCP Capital Requirements 348 Part IV Valuation Adjustments 13 Discounting and Collateral 355 13.1 Overview 355 13.2 The Starting Point 357 13.3 ColVA and Discounting 360 13.4 Beyond Perfect Collateralisation 374 14 CVA and DVA 379 14.1 Overview 379 14.2 Credit Valuation Adjustment 380 14.3 Debt Valuation Adjustment 388 14.4 Risk Mitigants 395 15 FVA 403 15.1 Overview 403 15.2 FVA Background 404 15.3 Portfolio FVA 423 16 Capital and KVA 437 16.1 Overview 437 16.2 Capital Valuation Adjustment 438 16.3 Management of KVA 451 16.4 KVA Overlaps 459 17 Initial Margin and MVA 463 17.1 Overview 463 17.2 Initial Margin Funding Costs 464 17.3 MVA Market Practice 474 17.4 MVA Overlaps 479 Part V Modelling and Management 18 Credit Curve Quantification 485 18.1 Proxy Curves 485 18.2 Loss Given Default 500 19 Managing xVA 507 19.1 The Role of An xVA Desk 507 19.2 Hedging 515 19.3 Operation of An xVA Desk 536 20 Quantifying Exposure: First-Generation Approaches 549 20.1 Overview 549 20.2 Monte Carlo Methodology 552 20.3 Choice of Models 561 20.4 Collateral Modelling 573 20.5 Examples 580 21 Quantifying Exposure: Second-Generation Approaches 599 21.1 Wrong-Way Risk I 599 21.2 Wrong-Way Risk II 610 21.3 Speeding Up xVA Calculations 619 21.4 Second-Generation xVAs (MVA and KVA) 632 21.5 Modelling Future Sensitivities 635 Glossary 645 General Terminology 649 References 651 Index 667