The xVA Challenge

The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital is a practical guide from one of the leading and most influential credit practitioners, Jon Gregory. Focusing on practical methods, this informative guide includes discussion around the latest regulatory requirements, market practice, and academic thinking. Beginning with a look at the emergence of counterparty risk during the recent global financial crisis, the discussion delves into the quantification of firm-wide credit exposure and risk mitigation methods, such as netting and collateral. It also discusses thoroughly the xVA terms, notably CVA, DVA, FVA, ColVA, and KVA and their interactions and overlaps. The discussion of other aspects such as wrong-way risks, hedging, stress testing, and xVA management within a financial institution are covered. The extensive coverage and detailed treatment of what has become an urgent topic makes this book an invaluable reference for any practitioner, policy maker, or student.

Counterparty credit risk and related aspects such as funding, collateral, and capital have become key issues in recent years, now generally characterized by the term 'xVA'. This book provides practical, in-depth guidance toward all aspects of xVA management.

• Market practice around counterparty credit risk and credit and debit value adjustment (CVA and DVA)
• The latest regulatory developments including Basel III capital requirements, central clearing, and mandatory collateral requirements
• The impact of accounting requirements such as IFRS 13
• Recent thinking on the applications of funding, collateral, and capital adjustments (FVA, ColVA and KVA)

The sudden realization of extensive counterparty risks has severely compromised the health of global financial markets. It's now a major point of action for all financial institutions, which have realized the growing importance of consistent treatment of collateral, funding, and capital alongside counterparty risk. The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital provides expert perspective and real-world guidance for today's institutions.

JON GREGORY 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 (CQR). Jon has a PhD from Cambridge University.

List of Spreadsheets xix

List of Appendices xxi

Acknowledgements xxiii

About the Author xxv

1 Introduction 1

2 The Global Financial Crisis 3

2.1 Pre-crisis 3

2.2 The crisis 5

2.3 Regulatory reform 8

2.4 Backlash and criticisms 8

2.5 A new world 10

3 The OTC Derivatives Market 11

3.1 The derivatives market 11

3.1.1 Derivatives 11

3.1.2 Exchange traded and OTC derivatives 12

3.1.3 Market size 12

3.1.4 Market participants 14

3.1.5 Credit derivatives 16

3.1.6 The dangers of derivatives 17

3.1.7 The Lehman experience 17

3.2 Derivative risks 18

3.2.1 Market risk 18

3.2.2 Credit risk 19

3.2.3 Operational and legal risk 19

3.2.4 Liquidity risk 20

3.2.5 Integration of risk types 20

3.2.6 Counterparty risk 20

3.3 Risk management of derivatives 20

3.3.1 Value-at-risk 20

3.3.2 Models 23

3.3.3 Correlation and dependency 23

4 Counterparty Risk 25

4.1 Background 25

4.1.1 Counterparty risk versus lending risk 25

4.1.2 Settlement and pre-settlement risk 26

4.1.3 Mitigating counterparty risk 28

4.1.4 Exposure and product type 29

4.1.5 Setups 31

4.2 Components 32

4.2.1 Mark-to-market and replacement cost 33

4.2.2 Credit exposure 33

4.2.3 Default probability, credit migration and credit spreads 34

4.2.4 Recovery and loss given default 35

4.3 Control and quantification 36

4.3.1 Credit limits 36

4.3.2 Credit value adjustment 38

4.3.3 CVA and credit limits 38

4.3.4 What does CVA represent? 39

4.3.5 Hedging counterparty risk 41

4.3.6 The CVA desk 42

4.4 Beyond CVA 43

4.4.1 Overview 43

4.4.2 Economic costs of an OTC derivative 43

4.4.3 xVA terms 44

4.5 Summary 46

5 Netting, Close-out and Related Aspects 47

5.1 Introduction 47

5.1.1 Overview 47

5.1.2 The need for netting and close-out 47

5.1.3 Payment and close-out netting 48

5.2 Default, netting and close-out 49

5.2.1 The ISDA Master Agreement 49

5.2.2 Events of default 49

5.2.3 Payment netting 50

5.2.4 Close-out netting 51

5.2.5 Product coverage and set-off rights 52

5.2.6 Close-out amount 53

5.2.7 The impact of netting 55

5.3 Multilateral netting and trade compression 56

5.3.1 Overview 56

5.3.2 Multilateral netting 56

5.3.3 Bilateral compression services 57

5.3.4 The need for standardisation 58

5.3.5 Examples 58

5.4 Termination features and resets 61

5.4.1 Walkaway features 61

5.4.2 Termination events 62

5.4.3 Reset agreements 64

5.5 Summary 65

6 Collateral 67

6.1 Introduction 67

6.1.1 Rationale for collateral 67

6.1.2 Analogy with mortgages 69

6.1.3 Variation margin and initial margin 69

6.2 Collateral terms 70

6.2.1 The credit support annex (CSA) 70

6.2.2 Types of CSA 71

6.2.3 Threshold 73

6.2.4 Initial margin 74

6.2.5 Minimum transfer amount and rounding 74

6.2.6 Haircuts 75

6.2.7 Linkage to credit quality 77

6.2.8 Credit support amount 78

6.2.9 Impact of collateral on exposure 79

6.3 Mechanics of collateral 80

6.3.1 Collateral call frequency 80

6.3.2 Valuation agents, disputes and reconciliations 81

6.3.3 Title transfer and security interest 82

6.3.4 Coupons, dividends and remuneration 83

6.4 Collateral and funding 84

6.4.1 Overview 84

6.4.2 Substitution 84

6.4.3 Rehypothecation 85

6.4.4 Segregation 87

6.4.5 Variation and initial margin rehypothecation and segregation 88

6.4.6 Standard CSA 89

6.5 Collateral usage 90

6.5.1 Extent of collateralisation 90

6.5.2 Coverage of collateralisation 91

6.5.3 Collateral type 92

6.6 The risks of collateral 93

6.6.1 Collateral impact outside OTC derivatives markets 93

6.6.2 Market risk and the margin period of risk 94

6.6.3 Operational risk 96

6.6.4 Legal risk 97

6.6.5 Liquidity risk 98

6.6.6 Funding liquidity risk 98

6.7 Regulatory collateral requirements 100

6.7.1 Background 100

6.7.2 Covered entities 101

6.7.3 General requirements 102

6.7.4 Haircuts 104

6.7.5 Segregation and rehypothecation 105

6.7.6 Initial margin calculations 105

6.7.7 Standardised initial margin method (SIMM) 106

6.8 Converting counterparty risk into funding liquidity risk 107

6.9 Summary 108

7 Credit Exposure and Funding 109

7.1 Credit exposure 109

7.1.1 Definition 109

7.1.2 Bilateral exposure 110

7.1.3 The close-out amount 111

7.1.4 Exposure as a short option position 111

7.1.5 Future exposure 112

7.1.6 Comparison to value-at-risk 113

7.2 Metrics for exposure 114

7.2.1 Expected future value 114

7.2.2 Potential future exposure 115

7.2.3 Expected exposure 116

7.2.4 EE and PFE for a normal distribution 116

7.2.5 Maximum PFE 117

7.2.6 Expected positive exposure 117

7.2.7 Negative exposure 118

7.2.8 Effective expected positive exposure (EEPE) 118

7.3 Factors driving exposure 119

7.3.1 Loans and bonds 119

7.3.2 Future uncertainty 120

7.3.3 Periodic cashflows 120

7.3.4 Combination of profiles 125

7.3.5 Optionality 126

7.3.6 Credit derivatives 128

7.4 The impact of netting and collateral on exposure 129

7.4.1 The impact of netting on future exposure 129

7.4.2 Netting and the impact of correlation 130

7.4.3 Netting and relative MTM 132

7.4.4 Impact of collateral on exposure 133

7.5 Funding, rehypothecation and segregation 135

7.5.1 Funding costs and benefits 135

7.5.2 Differences between funding and credit exposure 136

7.5.3 Impact of segregation and rehypothecation 136

7.5.4 Impact of collateral on credit and funding exposure 138

7.5.5 Examples 140

7.6 Summary 141

8 Capital Requirements and Regulation 143

8.1 Background to credit risk capital 144

8.1.1 Standardised approach 144

8.1.2 Internal ratings-based approach (IRB) 144

8.1.3 Double default 145

8.1.4 Exposure at default (EAD) 146

8.1.5 Incurred CVA 148

8.2 Current exposure method (CEM) 148

8.2.1 Add-ons 148

8.2.2 Netting and collateral treatment 149

8.3 The internal model method (IMM) 151

8.3.1 Background 151

8.3.2 The alpha factor and EEPE 151

8.4 Standardised approach for counterparty credit risk (SA-CCR) 153

8.4.1 Background 153

8.4.2 Basic approach 154

8.4.3 Netting 155

8.4.4 Collateral 156

8.4.5 Overcollateralisation and negative MTM 157

8.5 Comparison of EAD methods 157

8.5.1 Impact of maturity 157

8.5.2 Collateral 158

8.5.3 Negative MTM 159

8.5.4 Initial margin and threshold 159

8.5.5 Netting 160

8.6 Basel III 161

8.6.1 Overview 161

8.6.2 Stressed EPE 163

8.6.3 Increased margin period of risk 163

8.6.4 Backtesting 164

8.6.5 Wrong-way risk 166

8.6.6 Stress testing 167

8.7 CVA capital charge 168

8.7.1 Rationale 168

8.7.2 Standardised formula 169

8.7.3 Advanced approach 171

8.7.4 Example 174

8.7.5 Criticisms 176

8.7.6 US implementation 178

8.7.7 The European exemptions 178

8.8 Other important regulatory requirements 180

8.8.1 Fundamental review of the trading book 180

8.8.2 Leverage ratio 180

8.8.3 Floors 181

8.8.4 Liquidity coverage ratio and net stable funding ratio 182

8.8.5 Prudent value 182

8.9 Summary 183

9 Counterparty Risk Intermediation 185

9.1 Introduction 185

9.2 SPVs, DPCs, CDPCs and monolines 187

9.2.1 Default remoteness and “too big to fail” 187

9.2.2 Special purpose vehicles 187

9.2.3 Derivative product companies 188

9.2.4 Monolines and CDPCs 190

9.3 Central counterparties 192

9.3.1 The clearing mandate 193

9.3.2 OTC clearing 193

9.3.3 The CCP landscape 195

9.3.4 CCP risk management 196

9.3.5 Comparing bilateral and central clearing 199

9.3.6 Advantages and disadvantages of CCPs 200

9.3.7 CCP capital charges 201

9.3.8 What central clearing means for xVA 202

9.4 Summary 203

10 Quantifying Credit Exposure 205

10.1 Introduction 205

10.2 Methods for quantifying credit exposure 205

10.2.1 Parametric approaches 205

10.2.2 Semi-analytical methods 206

10.2.3 Monte Carlo simulation 209

10.3 Monte Carlo methodology 210

10.3.1 Simulation model 210

10.3.2 Scenario generation 211

10.3.3 Revaluation 212

10.3.4 Aggregation 215

10.3.5 Post-processing 215

10.3.6 Extraction 216

10.4 Real-world or risk-neutral 216

10.4.1 Two fundamentally different approaches 216

10.4.2 Drift 219

10.4.3 Volatility 220

10.4.4 Correlation 221

10.4.5 Market practice 221

10.5 Model choice 222

10.5.1 Risk-neutral or real-world? 222

10.5.2 Level of complexity 224

10.5.3 General comments 226

10.5.4 Correlations 227

10.6 Examples 228

10.6.1 Data set 228

10.6.2 Exposures profiles 230

10.7 Allocating exposure 235

10.7.1 Simple two-transaction, single-period example 235

10.7.2 Incremental exposure 237

10.7.3 Marginal exposure 240

10.8 Summary 243

11 Exposure and the Impact of Collateral 245

11.1 Overview 245

11.1.1 General impact of collateral 245

11.1.2 Modelling approach 246

11.2 Margin period of risk 247

11.2.1 Setup 247

11.2.2 Amortisation 248

11.2.3 Conditionality 249

11.2.4 Disputes 249

11.2.5 MPR discretisation and cashflows 250

11.2.6 MPR modelling 251

11.3 Numerical examples 252

11.3.1 Collateral assumptions 252

11.3.2 Margin period of risk impact 253

11.3.3 Simple approximations 255

11.3.4 Discretisation and cashflows 256

11.3.5 Impact of threshold 257

11.3.6 Do two-way CSAs always reduce exposure? 258

11.3.7 Non-cash collateral 260

11.3.8 Collateral and funding liquidity risk 261

11.4 Initial margin 262

11.4.1 Impact of initial margin on exposure 262

11.4.2 Dynamic initial margins 263

11.4.3 Segregation and funding exposure 264

11.5 Summary 265

12 Default Probabilities, Credit Spreads and Funding Costs 267

12.1 Overview 267

12.2 Default probability 267

12.2.1 Real-world and risk-neutral 267

12.2.2 The move to risk-neutral 269

12.2.3 Defining risk-neutral default probabilities 271

12.2.4 Term structure 272

12.2.5 Loss given default 273

12.3 Credit curve mapping 275

12.3.1 Overview 275

12.3.2 The CDS market 276

12.3.3 Loss given default 278

12.3.4 General approach 278

12.4 Generic curve construction 280

12.4.1 General approach 280

12.4.2 Third party curves 281

12.4.3 Mapping approach 282

12.4.4 Cross-sectional approach 283

12.4.5 Hedging 284

12.5 Funding curves and capital costs 285

12.5.1 Background 285

12.5.2 Funding costs 286

12.5.3 Defining a funding curve 286

12.5.4 Cost of capital 288

12.6 Summary 289

13 Discounting and Collateral 291

13.1 Overview 291

13.2 Discounting 291

13.2.1 Introduction 291

13.2.2 OIS rates 292

13.2.3 The risk-free rate 293

13.2.4 Perfect collateralisation and discounting 294

13.2.5 OIS discounting 295

13.2.6 OIS methodology 296

13.3 Beyond perfect collateralisation 297

13.3.1 The push towards perfect collateralisation 297

13.3.2 The xVA terms 297

13.4 Collateral valuation adjustments 300

13.4.1 Overview 300

13.4.2 Collateral rate adjustments 300

13.4.3 Collateral optionality 303

13.4.4 Non-cash collateral 307

13.4.5 The end of ColVA 307

13.5 Summary 308

14 Credit and Debt Value Adjustments 309

14.1 Overview 309

14.2 Credit value adjustment 309

14.2.1 Why CVA is not straightforward 309

14.2.2 History of CVA 310

14.2.3 CVA formula 311

14.2.4 CVA example 312

14.2.5 CVA as a spread 313

14.2.6 Exposure and discounting 313

14.2.7 Risk-neutrality 314

14.2.8 CVA semi-analytical methods 314

14.3 Impact of credit assumptions 315

14.3.1 Credit spread impact 315

14.3.2 Recovery impact 316

14.4 CVA allocation and pricing 317

14.4.1 Netting and incremental CVA 317

14.4.2 Incremental CVA example 319

14.4.3 Marginal CVA 319

14.4.4 CVA as a spread 321

14.4.5 Numerical issues 321

14.5 CVA with collateral 323

14.5.1 Impact of margin period of risk 324

14.5.2 Thresholds and initial margins 324

14.6 Debt value adjustment 326

14.6.1 Overview 326

14.6.2 Accounting standards and DVA 326

14.6.3 DVA and pricing 327

14.6.4 Bilateral CVA formula 327

14.6.5 Close-out and default correlation 328

14.6.6 Example 330

14.6.7 DVA and own-debt 331

14.6.8 DVA in derivatives 332

14.7 Summary 334

15 Funding Value Adjustment 335

15.1 Funding and derivatives 335

15.1.1 Why there are funding costs and benefits 335

15.1.2 The nature of funding costs and benefits 336

15.1.3 Relationship to CVA and DVA 338

15.1.4 FVA in financial statements 339

15.2 Funding value adjustment 341

15.2.1 Intuitive definition 341

15.2.2 Discounting approach 343

15.2.3 More complex cases 345

15.2.4 Contingent FVA 347

15.2.5 Allocation of FVA 348

15.3 The practical use of FVA 349

15.3.1 Link to DVA 349

15.3.2 CVA/DVA/FVA framework 350

15.3.3 Is FVA really symmetric? 351

15.3.4 Defining the funding rate 351

15.3.5 The Hull and White and accounting arguments 352

15.3.6 Resolving the FVA debate 354

15.3.7 Remaining issues 355

15.3.8 Example 356

15.4 Summary 357

16 LCH/CME Basis and Capital Value Adjustments 359

16.1 Overview 359

16.2 Margin value adjustment 360

16.2.1 Rationale 360

16.2.2 IM profiles 361

16.2.3 MVA formula 364

16.2.4 Example 365

16.3 Capital value adjustment 366

16.3.1 Rationale 366

16.3.2 Capital profiles 368

16.3.3 Formula 369

16.3.4 Term structure behaviour 370

16.3.5 Behavioural aspects and regulatory change 371

16.3.6 Example 372

16.3.7 KVA and MVA 373

16.3.8 Overlaps and hedging 374

16.3.9 KVA reporting 375

16.4 Summary 375

17 Wrong-way Risk 377

17.1 Overview 377

17.2 Overview of wrong-way risk 377

17.2.1 Simple example 377

17.2.2 Classic example and empirical evidence 378

17.2.3 General and specific WWR 379

17.2.4 WWR challenges 380

17.3 Quantification of wrong-way risk 380

17.3.1 Wrong-way risk and CVA 380

17.3.2 Simple example 381

17.3.3 Wrong-way collateral 382

17.4 Wrong-way risk modelling approaches 383

17.4.1 Hazard rate approaches 383

17.4.2 Structural approaches 385

17.4.3 Parametric approach 387

17.4.4 Jump approaches 388

17.4.5 Credit derivatives 390

17.4.6 Wrong-way risk and collateral 391

17.4.7 Central clearing and wrong-way risk 393

17.5 Summary 395

18 xVA Management 397

18.1 Introduction 397

18.2 The role of an xVA desk 397

18.2.1 Motivation 397

18.2.2 Role 398

18.2.3 Profit centre or utility? 399

18.2.4 Operation and rollout 400

18.3 Hedging xVA 403

18.3.1 Motivation 403

18.3.2 xVA as an exotic option 403

18.3.3 Misalignment 404

18.3.4 Market risk 405

18.3.5 Credit, funding and capital hedging 406

18.3.6 Cross-gamma 406

18.3.7 P&L explain 407

18.3.8 Capital relief from hedges 407

18.3.9 Market practice and hedging 411

18.4 xVA systems 412

18.4.1 Overview 412

18.4.2 Optimisations 413

18.4.3 Shared or separate implementations 414

18.4.4 Internal and vendor systems 416

18.4.5 IMM approval 418

18.5 Summary 419

19 xVA Optimisation 421

19.1 Overview 421

19.2 Market practice 422

19.2.1 General approach to xVA 422

19.2.2 Totem 424

19.3 Examples 425

19.3.1 xVA assumptions 425

19.3.2 Uncollateralised 426

19.3.3 Off-market 427

19.3.4 Partially collateralised 428

19.3.5 One-way collateralised 429

19.3.6 Collateralised 430

19.3.7 Overcollateralised (initial margin) and backloading 430

19.4 Costs and the balance of xVA terms 433

19.4.1 Spectrum of transaction 433

19.4.2 Optimising xVA 434

19.4.3 Impact of credit quality and maturity 436

19.4.4 Summary 437

19.5 xVA optimisation 437

19.5.1 Intermediation 437

19.5.2 Restrikes 438

19.5.3 Uncollateralised to collateralised 439

19.5.4 Backloading to a CCP 440

19.6 Summary 441

20 The Future 443

Glossary 445

References 447

Index 457

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