The xVA Challenge

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