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.
Table of Contents
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
