The xVA Challenge, Fourth Edition - Counterparty Risk, Funding, Collateral,

Description: A thoroughly updated and expanded edition of the xVA challenge The period since the global financial crisis has seen a major re-appraisal of derivatives valuation, generally expressed in the form of valuation adjustments ('xVAs'). The quantification of xVA is now seen as fundamental to derivatives pricing and valuation. The xVA topic has been complicated and further broadened by accounting standards and regulation. All users of derivatives need to have a good understanding of the implications of xVA. The pricing and valuation of the different xVA terms has become a much studied topic and many aspects are in constant debate both in industry and academia. * Discussing counterparty credit risk in detail, including the many risk mitigants, and how this leads to the different xVA terms * Explains why banks have undertaken a dramatic reappraisal of the assumptions they make when pricing, valuing and managing derivatives * Covers what the industry generally means by xVA and how it is used by banks, financial institutions and end-users of derivatives * Explains all of the underlying regulatory capital (e.g. SA-CCR, SA-CVA) and liquidity requirements (NSFR and LCR) and their impact on xVA * Underscores why banks have realised the significant impact that funding costs, collateral effects and capital charges have on valuation * Explains how the evolution of accounting standards to cover CVA, DVA, FVA and potentially other valuation adjustments * Explains all of the valuation adjustments - CVA, DVA, FVA, ColVA, MVA and KVA - in detail and how they fit together * Covers quantification of xVA terms by discussing modelling and implementation aspects. Taking into account the nature of the underlying market dynamics and new regulatory environment, this book brings readers up to speed on the latest developments on the topic. List of Spreadsheets xix List of Appendices xxi Acknowledgements xxiii About the Author xxv Section 1 Basics 1 Introduction 3 2 Derivatives 5 2.1 Introduction 5 2.2 The Derivatives Market 6 2.2.1 Exchange-traded and OTC Derivatives 6 2.2.2 Clearing 8 2.2.3 Market Overview 9 2.2.4 Market Participants and Collateralisation 11 2.2.5 Banks and End Users 14 2.2.6 ISDA Documentation 16 2.2.7 Credit Derivatives 17 2.2.8 Financial Weapons of Mass Destruction 18 2.2.9 The Lehman Brothers Bankruptcy 19 2.3 Derivative Risks 20 2.3.1 Market Risk 21 2.3.2 Credit Risk 21 2.3.3 Operational and Legal Risk 22 2.3.4 Liquidity Risk 22 2.3.5 Integration of Risk Types 23 2.3.6 Counterparty Risk 23 2.4 Systemic Risk of Derivatives 24 2.4.1 Overview 24 2.4.2 Special Purpose Vehicles 24 2.4.3 Derivatives Product Companies 25 2.4.4 Monolines and CDPCs 26 2.5 The Global Financial Crisis and Central Clearing of OTC Derivatives 28 2.5.1 OTC Derivatives and the Crisis 28 2.5.2 OTC Derivatives Clearing 29 2.5.3 CCPs in the Global Financial Crisis 31 2.5.4 The Clearing Mandate 32 2.5.5 Bilateral Margin Requirements 33 2.5.6 CCPs in Context 34 2.6 Derivatives Risk Modelling 36 2.6.1 Value-at-risk 36 2.6.2 Models 38 2.6.3 Correlation and Dependency 39 3 Counterparty Risk and Beyond 41 3.1 Counterparty Risk 41 3.1.1 Counterparty Risk Versus Lending Risk 41 3.1.2 Settlement, Pre-settlement, and Margin Period of Risk 42 3.1.3 Mitigating Counterparty Risk 45 3.1.4 Product Type 46 3.1.5 Credit Limits 48 3.1.6 Credit Value Adjustment 50 3.1.7 What Does CVA Represent? 51 3.1.8 Hedging Counterparty Risk and the CVA Desk 52 3.2 Beyond Counterparty Risk 54 3.2.1 Overview 54 3.2.2 Economic Costs of a Derivative 54 3.2.3 xVA Terms 55 3.3 Components of xVA 57 3.3.1 Overview 57 3.3.2 Valuation and Mark-to-market 57 3.3.3 Replacement Cost and Credit Exposure 58 3.3.4 Default Probability, Credit Migration, and Credit Spreads 59 3.3.5 Recovery and Loss Given Default 60 3.3.6 Funding, Collateral, and Capital Costs 61 4 Regulation 63 4.1 Regulation and the Global Financial Crisis 63 4.2 Capital Requirements 64 4.2.1 Overview 64 4.2.2 Capital Ratios 65 4.2.3 Risk Type 67 4.2.4 Market Risk Capital 68 4.2.5 CVA Capital 69 4.2.6 CCR Capital 70 4.2.7 Leverage Ratio 70 4.2.8 Capital Floors 71 4.2.9 Large Exposure Framework 72 4.2.10 Bank Stress Tests 73 4.2.11 Prudent Valuation 73 4.3 Liquidity 73 4.3.1 Overview 73 4.3.2 High-quality Liquid Assets 74 4.3.3 Liquidity Coverage Ratio 75 4.3.4 Net Stable Funding Ratio 76 4.4 Clearing and Margining 77 4.4.1 Central Clearing 77 4.4.2 Bilateral Margin Requirements 81 4.4.3 Exemptions 82 4.4.4 CCP Capital Requirements 84 5 What is xVA? 85 5.1 Overview 85 5.2 Analysis of xVA 86 5.2.1 Definition 86 5.2.2 Components 86 5.2.3 Why Valuation Adjustments? 87 5.2.4 Mark-to-market and xVA as a Cost (and Benefit) 88 5.2.5 xVAs by Transaction Type 90 5.2.6 Overlaps and Portfolio Effects 91 5.2.7 CVA is the Least Real Valuation Adjustment 92 5.3 Valuation 93 5.3.1 Price and Value 93 5.3.2 xVA Markets 94 5.3.3 Accounting Standards 95 5.3.4 Accounting Trends 98 5.3.5 Totem 99 5.3.6 Contractual Terms and Value 100 5.4 Pricing 100 5.4.1 Reality or Creating the Right Incentive? 100 5.4.2 Approach for Capital 101 5.4.3 Approach to Regulatory Ratios 102 5.4.4 Lack of Arbitrage 104 5.4.5 Entry and Exit Pricing 105 5.4.6 xVA Quantification 106 5.4.7 Special Cases 106 Section 2 Risk Mitigation 6 Netting, Close-Out, and Related Aspects 111 6.1 Overview 111 6.2 Cash Flow Netting 112 6.2.1 Payment Netting 112 6.2.2 Currency Netting and CLS 113 6.2.3 Clearing Rings 114 6.2.4 Portfolio Compression 115 6.2.5 Compression Algorithm 118 6.2.6 Benefits of Cashflow Netting 120 6.3 Value Netting 121 6.3.1 Overview 121 6.3.2 Close-out Netting 121 6.3.3 Payment Under Close-out 122 6.3.4 Close-out and xVA 124 6.3.5 ISDA Definitions 125 6.3.6 Set-off 129 6.4 The Impact of Netting 130 6.4.1 Risk Reduction 130 6.4.2 The Impact of Netting 131 6.4.3 Multilateral Netting and Bifurcation 132 6.4.4 Netting Impact on Other Creditors 135 7 Margin (Collateral) and Settlement 137 7.1 Termination and Reset Features 137 7.1.1 Break Clauses 137 7.1.2 Resettable Transactions 140 7.2 Basics of Margin/Collateral 141 7.2.1 Terminology 141 7.2.2 Rationale 142 7.2.3 Variation Margin and Initial Margin 144 7.2.4 Method of Transfer and Remuneration 145 7.2.5 Rehypothecation and Segregation 147 7.2.6 Settle to Market 150 7.2.7 Valuation Agent, Disputes, and Reconciliations 151 7.3 Margin Terms 152 7.3.1 The Credit Support Annex 152 7.3.2 Types of CSA 153 7.3.3 Margin Call Frequency 154 7.3.4 Threshold, Initial Margin, and the Minimum Transfer Amount 155 7.3.5 Margin Types and Haircuts 157 7.3.6 Credit Support Amount Calculations 161 7.3.7 Impact of Margin on Exposure 163 7.3.8 Traditional Margin Practices in Bilateral and Centrally-cleared Markets 165 7.4 Bilateral Margin Requirements 166 7.4.1 General Requirements 166 7.4.2 Phase-in and Coverage 168 7.4.3 Initial Margin and Haircut Calculations 169 7.4.4 Eligible Assets and Haircuts 171 7.4.5 Implementation and Impact of the Requirements 172 7.5 Impact of Margin 173 7.5.1 Impact on Other Creditors 173 7.5.2 Market Risk and Margin Period of Risk 174 7.5.3 Liquidity, FX, and Wrong-way Risks 178 7.5.4 Legal and Operational Risks 179 7.6 Margin and Funding 180 7.6.1 Overview 180 7.6.2 Margin and Funding Liquidity Risk 181 8 Central Clearing 185 8.1 Evolution of Central Clearing 185 8.1.1 Exchange Trading 185 8.1.2 Evolution of Complete Clearing 186 8.1.3 What is a CCP? 187 8.2 Mechanics of Central Clearing 189 8.2.1 Landscape 189 8.2.2 Novation 191 8.2.3 Multilateral Offset and Compression 192 8.2.4 Margin and Default Funds 194 8.2.5 Clearing Relationships 195 8.3 CCP Risk Management 197 8.3.1 Overview and Membership Requirements 197 8.3.2 Margin 198 8.3.3 Default Scenarios and Margin Period of Risk 199 8.3.4 The Loss Waterfall 202 8.3.5 Comparing Bilateral and Central Clearing 204 8.4 Initial Margin and Default Funds 205 8.4.1 Coverage of Initial Margin and Default Funds 205 8.4.2 Default Fund Versus Initial Margin 206 8.4.3 Default Fund Coverage 207 8.5 Impact of Central Clearing 209 8.5.1 Advantages and Disadvantages of Central Clearing 209 8.5.2 Will Mandatory Clearing Kill Credit Value Adjustment? 210 9 Initial Margin Methodologies 213 9.1 Role of Initial Margin 213 9.1.1 Purpose 213 9.1.2 Margin Period of Risk 215 9.1.3 Coverage: Quantitative and Qualitative 217 9.1.4 Haircuts 218 9.1.5 Linkage to Credit Quality 218 9.1.6 Cross-margining 220 9.2 Initial Margin Approaches 222 9.2.1 Simple Approaches 222 9.2.2 SPAN® 223 9.2.3 Value-at-risk and Expected Shortfall 227 9.3 Historical Simulation 229 9.3.1 Overview 229 9.3.2 Look-back Period 230 9.3.3 Relative and Absolute Returns 231 9.3.4 Volatility Scaling 233 9.3.5 Procyclicality 234 9.3.6 Current CCP Methodologies 239 9.3.7 Computational Considerations 241 9.4 Bilateral Margin and SIMM 242 9.4.1 Overview 242 9.4.2 Standard Schedules 244 9.4.3 Variance-covariance Approaches 245 9.4.4 The ISDA SIMM 249 9.4.5 Implementation of Bilateral Margin Requirements 252 10 The Impact and Risk of Clearing and Margining 255 10.1 Risks of Central Clearing 256 10.1.1 Historical CCP Problems 256 10.1.2 The 1987 Stock Market Crash 258 10.1.3 The 2018 Nasdaq Case 259 10.1.4 Risks Faced by CCPs 260 10.1.5 Risks Caused by CCPs 261 10.2 Analysis of a CCP Loss Structure 262 10.2.1 Review of the Loss Waterfall 262 10.2.2 Impact of Default Fund Exposure 264 10.2.3 The Prisoner's Dilemma and AIPs 265 10.2.4 Other Loss Allocation Methods 267 10.3 Impact of Margin 271 10.3.1 Background and Historical Examples 271 10.3.2 Variation Margin 273 10.3.3 Initial Margin 275 10.3.4 Cost and xVA 276 10.3.5 Seniority 277 10.3.6 Bilateral and Cleared Markets 277 Section 3 Building Blocks 11 Future Value and Exposure 283 11.1 Credit Exposure 283 11.1.1 Positive and Negative Exposure 283 11.1.2 Definition of Value 284 11.1.3 Current and Potential Future Exposure 285 11.1.4 Nature of Exposure 286 11.1.5 Metrics 288 11.2 Drivers of Exposure 292 11.2.1 Future Uncertainty 292 11.2.2 Cash Flow Frequency 293 11.2.3 Curve Shape 294 11.2.4 Moneyness 297 11.2.5 Combination of Profiles 298 11.2.6 Optionality 299 11.2.7 Credit Derivatives 300 11.3 Aggregation, Portfolio Effects, and the Impact of Collateralisation 302 11.3.1 The Impact of Aggregation on Exposure 302 11.3.2 Off-market Portfolios 304 11.3.3 Impact of Margin 305 11.4 Funding, Rehypothecation, and Segregation 308 11.4.1 Funding Costs and Benefits 308 11.4.2 Differences Between Funding and Credit Exposure 309 11.4.3 Impact of Segregation and Rehypothecation 310 11.4.4 Impact of Margin on Exposure and Funding 312 12 Credit Spreads, Default Probabilities, and LGDs 315 12.1 Default Probability 315 12.1.1 Real World and Risk Neutral 315 12.1.2 CVA and Risk-neutral Default Probabilities 316 12.1.3 Defining Risk-neutral Default Probabilities 319 12.1.4 Loss Given Default 321 12.2 Credit Curve Mapping 323 12.2.1 Overview 323 12.2.2 The CDS Market 324 12.2.3 Loss Given Default 326 12.2.4 General Approach 327 12.3 Generic Curve Construction 330 12.3.1 General Approach 330 12.3.2 Intersection (Bucketing) Approach 332 12.3.3 Cross-section Methodology 334 12.3.4 Curve Shape, Interpolation, and Indices 336 12.3.5 Third-party Providers 337 12.3.6 Hedging 338 13 Regulatory Methodologies 339 13.1 Overview 339 13.2 Credit Risk (Default Risk) Capital 341 13.2.1 Standardised Approach 341 13.2.2 Internal Ratings-based Approach 342 13.2.3 Guarantees 343 13.3 CVA (Market Risk) Capital 343 13.3.1 The CVA Capital Charge 343 13.3.2 Standardised CVA Risk Capital Charge 344 13.3.3 BA-CVA 345 13.3.4 Advanced CVA Capital Risk Charge 348 13.3.5 SA-CVA 351 13.3.6 Capital Relief and EU Exemptions 355 13.4 Exposure Calculation Methodologies 356 13.4.1 Exposure at Default 356 13.4.2 Current Exposure Method 358 13.4.3 Standardised Approach for Counterparty Credit Risk 361 13.4.4 Broader Impact of SA-CCR 366 13.4.5 The Internal Model Method 367 13.4.6 The Leverage Ratio 372 13.4.7 Wrong-way Risk 373 13.5 Examples 374 13.5.1 Comparison of EAD Methods 374 13.5.2 Comparison of Capital Charges 377 13.5.3 Impact of Hedges 379 13.6 Central Counterparty Capital Requirements 384 13.6.1 Background 384 13.6.2 Trade Exposure 385 13.6.3 Default Fund Exposure 385 13.6.4 Client Clearing 386 14 Funding, Margin, and Capital Costs 389 14.1 Bank Financing 389 14.2 Capital 391 14.2.1 Minimum Capital Ratios and Capital Costs 391 14.2.2 Leverage Ratio 393 14.2.3 Cost of Capital 394 14.3 Funding 394 14.3.1 Overview 394 14.3.2 Cost of Funding 398 14.3.3 The Risk-free Rate, IBOR, and OIS 400 14.3.4 IBOR Transition 402 14.3.5 Funding Spreads 403 14.3.6 NSFR and LCR 406 14.3.7 Accounting 406 15 Quantifying Exposure 409 15.1 Methods for Quantifying Exposure 409 15.1.1 Overview 409 15.1.2 Parametric Approaches 410 15.1.3 Semianalytical Methods 411 15.1.4 Monte Carlo Simulation 414 15.2 Exposure Allocation 414 15.2.1 Overview 414 15.2.2 Incremental and Marginal Exposure 414 15.2.3 Impact of Dependency 417 15.3 Monte Carlo Methodology 419 15.3.1 Basic Framework 419 15.3.2 Revaluation, Cash Flow Bucketing, and Scaling 421 15.3.3 Risk-neutral or Physical Measure 423 15.3.4 Aggregation Level 429 15.4 Choice of Models 430 15.4.1 Overview 430 15.4.2 Interest Rates 432 15.4.3 Foreign Exchange 435 15.4.4 Other Asset Classes 437 15.4.5 Correlations, Proxies, and Extrapolation 437 15.5 Modelling Margin (Collateral) 439 15.5.1 Overview 439 15.5.2 Margin Period of Risk 441 15.5.3 Modelling Approach 442 15.5.4 Initial Margin 445 15.6 Examples 448 15.6.1 Interest Rate Swap Example 448 15.6.2 Trade-level Exposures 450 15.6.3 Portfolio Exposures 452 15.6.4 Notional Resets 456 15.6.5 Impact of Variation Margin 457 15.6.6 Impact of Initial Margin 460 Section 4 The xVAs 16 The Starting Point and Discounting 465 16.1 The Starting Point 465 16.1.1 Basic Valuation 465 16.1.2 Perfect Collateralisation 466 16.1.3 Collateral or OIS Discounting 467 16.2 ColVA and Discounting 469 16.2.1 Definition of ColVA 469 16.2.2 Asymmetry 470 16.2.3 Cheapest-to-deliver Optionality 473 16.2.4 Non-cash Margin 478 16.2.5 The End of ColVA 479 16.3 Beyond Perfect Collateralisation - xVA 480 16.3.1 Overview 480 16.3.2 Definition of xVA Terms 482 17 CVA 485 17.1 Overview 485 17.2 Credit Value Adjustment 486 17.2.1 CVA Compared to Traditional Credit Pricing 486 17.2.2 Direct and Path-wise CVA Formulas 487 17.2.3 CVA as a Spread 492 17.2.4 Special Cases 493 17.2.5 Credit Spread Effects 493 17.2.6 Loss Given Default 495 17.3 Debt Value Adjustment 498 17.3.1 Accounting Background 498 17.3.2 DVA, Price, and Value 499 17.3.3 Bilateral CVA Formula 500 17.3.4 Close-out and Default Correlation 502 17.3.5 The Use of DVA 503 17.4 CVA Allocation 506 17.4.1 Incremental CVA 506 17.4.2 Marginal CVA 509 17.5 Impact of Margin 510 17.5.1 Overview 510 17.5.2 Example 511 17.5.3 Initial Margin 512 17.5.4 CVA to CCPs 513 17.6 Wrong-way Risk 514 17.6.1 Overview 514 17.6.2 Quantification of WWR in CVA 516 17.6.3 Wrong-way Risk Models 518 17.6.4 Jump Approaches 522 17.6.5 Credit Derivatives 524 17.6.6 Collateralisation and WWR 525 17.6.7 Central Clearing and WWR 526 18 FVA 529 18.1 Overview 529 18.2 FVA and Discounting 530 18.2.1 Market Practice 530 18.2.2 Source of Funding Costs and Benefits 531 18.2.3 Definition of FVA 534 18.2.4 Symmetric FVA Formula 535 18.2.5 CVA/DVA/FVA Framework 539 18.2.6 The FVA Debate 546 18.2.7 Funding Costs and FVA Accounting 548 18.3 Asymmetric FVA 551 18.3.1 Overview 551 18.3.2 Asymmetric FVA 552 18.3.3 FVA Allocation 555 18.3.4 NSFR Invariance 558 18.3.5 Funding Strategies 560 18.3.6 LCR Costs 561 18.3.7 Funding and Wrong-way Risk 563 19 KVA 565 19.1 Overview 565 19.2 Capital Value Adjustment (KVA) 566 19.2.1 Return on Capital 566 19.2.2 KVA Formula 567 19.2.3 Capital Profiles 568 19.2.4 KVA Example 572 19.2.5 Implementation of KVA 573 19.2.6 The Leverage Ratio 575 19.3 Management of KVA 577 19.3.1 Current Treatment of KVA by Banks 577 19.3.2 Optimal KVA Management 580 19.3.3 Discounting 585 19.3.4 KVA Accounting 585 19.4 KVA Overlaps 587 19.4.1 CVA and KVA 587 19.4.2 FVA and KVA 589 20 MVA 591 20.1 Overview 591 20.2 Initial Margin Funding Costs 594 20.2.1 Introduction 594 20.2.2 MVA Formula 594 20.2.3 EIM Term 595 20.2.4 Computation Challenges 599 20.2.5 Pricing and MVA Example 600 20.3 MVA 602 20.3.1 A Need to Charge MVA? 602 20.3.2 Accounting MVA 603 20.3.3 Contingent MVA 603 20.3.4 CCP Basis 604 20.4 Link to KVA 606 20.4.1 Overview 606 20.4.2 Example 607 21 Actively Managing xVA and the Role of an xVA Desk 609 21.1 The Role of an xVA Desk 609 21.1.1 Motivation 609 21.1.2 Charging Structure and Coverage 611 21.1.3 Time Decay 614 21.1.4 Profit Centre or Utility? 615 21.1.5 Pricing 617 21.2 Hedging 619 21.2.1 Overview 619 21.2.2 Sensitivities 621 21.2.3 Gamma, Cross-gamma, Tail Risk, and Rebalancing 625 21.2.4 Market Practice 627 21.2.5 Jump to Default Risk 629 21.2.6 Beta Hedging 630 21.2.7 Risk Limits and P&L Explain 631 21.2.8 Examples 633 21.2.9 Impact on Capital 634 21.2.10 Pushing xVA into Base Value 638 21.3 Operation of an xVA Desk 638 21.3.1 Interaction with a Treasury 638 21.3.2 Capital 640 21.3.3 Systems and Quantification 641 21.3.4 xVA Optimisation 645 Glossary 649 References 653 Index 667

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