John Wiley & Sons The xVA Challenge Cover A thoroughly updated and expanded edition of the xVA challenge The period since the global financia.. Product #: 978-1-119-50897-7 Regular price: $76.10 $76.10 In Stock

The xVA Challenge

Counterparty Risk, Funding, Collateral, Capital and Initial Margin

Gregory, Jon

Wiley Finance Editions

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4. Edition May 2020
704 Pages, Hardcover
Practical Approach Book

ISBN: 978-1-119-50897-7
John Wiley & Sons

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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
JON GREGORY, PHD, is an independent expert specialising in counterparty risk and related aspects. He has worked on many aspects of credit risk in his career, being previously with Barclays Capital, BNP Paribas and Citigroup. He is a senior advisor for Solum Financial Derivatives Advisory and is a faculty member for the Certificate of Quantitative Finance (CQF). Jon has a PhD from Cambridge University.

J. Gregory, Independent Trainer and Consultant