Counterparty Credit Risk: The new challenge for global financial markets (The Wiley Finance Series)

The first decade of the 21st Century has been disastrous for financial institutions, derivatives and risk management. Counterparty credit risk has become the key element of financial risk management, highlighted by the bankruptcy of the investment bank Lehman Brothers and failure of other high profile institutions such as Bear Sterns, AIG, Fannie Mae and Freddie Mac. The sudden realisation of extensive counterparty risks has severely compromised the health of global financial markets. Counterparty risk is now a key problem for all financial institutions. This book explains the emergence of counterparty risk during the recent credit crisis. The quantification of firm-wide credit exposure for trading desks and businesses is discussed alongside risk mitigation methods such as netting and collateral management (margining). Banks and other financial institutions have been recently developing their capabilities for pricing counterparty risk and these elements are considered in detail via a characterisation of credit value adjustment (CVA). The implications of an institution valuing their own default via debt value adjustment (DVA) are also considered at length. Hedging aspects, together with the associated instruments such as credit defaults swaps (CDSs) and contingent CDS (CCDS) are described in full. A key feature of the credit crisis has been the realisation of wrong-way risks illustrated by the failure of monoline insurance companies. Wrong-way counterparty risks are addressed in detail in relation to interest rate, foreign exchange, commodity and, in particular, credit derivative products. Portfolio counterparty risk is covered, together with the regulatory aspects as defined by the Basel II capital requirements. The management of counterparty risk within an institution is also discussed in detail. Finally, the design and benefits of central clearing, a recent development to attempt to control the rapid growth of counterparty risk, is considered. This book is unique in being practically focused but also covering the more technical aspects. It is an invaluable complete reference guide for any market practitioner with any responsibility or interest within the area of counterparty credit risk. Counterparty Credit Risk: The New Challenge for Global Financial Markets......Page 5 Contents......Page 7 Acknowledgements......Page 19 List of Spreadsheets......Page 20 List of Abbreviations......Page 21 Introduction......Page 23 1.1.1 Market risk......Page 27 1.1.4 Credit risk......Page 28 1.1.6 Disadvantages of value-at-risk......Page 29 1.2.1 Why models?......Page 30 1.2.2 Good model, bad model......Page 31 1.3.2 Market structure......Page 32 1.4.1 Too big to fail......Page 33 1.4.3 Compensation culture......Page 34 1.5.1 What is counterparty risk?......Page 35 1.5.3 Counterparty risk and integration of risk types......Page 36 1.5.4 Counterparty risk and today’s derivatives market......Page 37 2.1.1 Origins of counterparty risk......Page 39 2.1.4 OTC derivatives......Page 40 2.1.5 Counterparty risk......Page 42 2.1.6 Counterparty risk versus lending risk......Page 43 2.1.7 Mitigating counterparty risk......Page 44 2.1.8 Counterparty risk players......Page 45 2.2.1 Credit exposure......Page 46 2.2.2 Default probability and credit migration......Page 47 2.2.4 Mark-to-market......Page 48 2.2.6 Exposure......Page 49 2.2.8 Potential future exposure (PFE)......Page 50 2.3.1 Trading with high-quality counterparties......Page 51 2.3.2 Cross-product netting......Page 52 2.3.4 Collateralisation......Page 53 2.3.5 Walkaway features......Page 54 2.3.8 Exchanges and centralised clearing houses......Page 55 2.4.1 Credit lines......Page 56 2.4.2 Pricing counterparty risk......Page 58 2.4.3 Hedging counterparty risk......Page 59 2.4.4 Capital requirements and counterparty risk......Page 60 2.5.2 Expected exposure......Page 61 2.5.5 Overview of exposure metrics......Page 62 2.5.6 Expected positive exposure......Page 63 2.6 Summary......Page 64 Appendix 2.A Characterising exposure for a normal distribution......Page 65 3.1.1 Two-way or one-way agreements......Page 67 3.2.2 Special purpose vehicles......Page 68 3.2.3 Central counterparties......Page 69 3.3.1 Termination events......Page 70 3.3.3 Walkaway features......Page 71 3.4 Netting and close-out......Page 72 3.4.1 Close-out......Page 73 3.4.3 The need for close-out netting......Page 74 3.4.6 The ISDA Master Agreement......Page 76 3.4.9 Advantages and disadvantages of netting......Page 77 3.4.10 Multilateral netting......Page 79 3.5.1 Negativity of MtM......Page 80 3.5.2 Impact of correlation......Page 81 3.5.3 Negative MtM of a netting set......Page 83 3.5.4 Positive MtM of a netting set......Page 84 3.6 Collateral......Page 85 3.6.1 The basics of collateralisation......Page 86 3.6.3 Setting up a collateral agreement......Page 87 3.6.4 Valuation agent......Page 88 3.6.6 Coverage of collateralisation......Page 89 3.6.7 Disputes and reconciliations......Page 90 3.7.1 Linkage of collateral parameters to credit quality......Page 91 3.7.3 Threshold......Page 92 3.7.4 Independent amount......Page 93 3.7.7 Haircuts......Page 94 3.7.8 Coupons and interest payments......Page 96 3.7.10 Call-and-return example......Page 97 3.8 Is risk mitigation always a good thing?......Page 99 Appendix 3.A EE of independent normal variables......Page 100 4.1 Quantifying credit exposure......Page 103 4.1.1 Mark-to-market + add-ons......Page 104 4.1.2 Semi-analytical methods......Page 105 4.1.3 Monte Carlo simulation......Page 106 4.1.4 Roll-off risk......Page 108 4.2.2 Swaps......Page 110 4.2.4 Options......Page 111 4.2.5 Credit derivatives......Page 112 4.2.7 Exercise dates......Page 115 4.3 Models for credit exposure......Page 116 4.3.2 Risk-neutral or real?......Page 117 4.3.3 Equities......Page 119 4.3.6 Credit spreads......Page 120 4.3.7 Interest rates......Page 121 4.3.8 Advanced models......Page 122 4.3.10 Correlations......Page 123 4.4.1 Modelling netting......Page 124 4.4.3 Examples......Page 125 4.5 Exposure contributions......Page 127 4.5.2 Simple two-trade marginal EE example......Page 128 4.5.3 Marginal EE and correlation......Page 129 4.6 Summary......Page 130 Appendix 4.A Semi-analytical formula for exposure of a forward contract......Page 131 Appendix 4.B Computing marginal EE......Page 132 5.2.1 Remargin period......Page 133 5.2.2 Potential future exposure with collateral......Page 135 5.2.4 Collateral volatility......Page 136 5.2.5 Correlation between collateral and exposure......Page 137 5.3 Modelling collateral......Page 138 5.3.1 Parameters......Page 139 5.4.1 Parameters......Page 140 5.4.2 Scenarios......Page 141 5.4.3 Exposure distributions......Page 142 5.4.4 Simple approximation – idealised case......Page 143 5.4.5 Simple approximation – impact of minimum transfer amount......Page 145 5.4.6 Impact of threshold......Page 146 5.4.7 Simple approximation – impact of threshold......Page 147 5.4.8 Operational cost versus reduction of exposure......Page 148 5.5.1 Operational risk......Page 149 5.5.4 Liquidity and liquidation risk......Page 150 Appendix 5.A Calculation of collateralised PFE (cash collateral)......Page 151 Appendix 5.C Mathematical treatment of a collateralised exposure......Page 152 6.1 Defaults, recovery rates, credit spreads and credit derivatives......Page 155 6.1.2 Recovery rates......Page 156 6.1.3 Credit spreads......Page 158 6.2.1 Market growth and uses......Page 159 6.2.2 Credit default swaps (CDSs)......Page 160 6.2.4 Asset swaps......Page 161 6.2.5 Linkage between bonds, asset swaps and CDS premiums......Page 162 6.2.7 Fixed and digital CDSs and recovery swaps......Page 164 6.3.2 Credit events......Page 165 6.3.3 Settlement of CDS......Page 166 6.3.4 Cheapest-to-deliver option and restructuring......Page 167 6.3.5 Delivery squeeze......Page 169 6.3.6 CDS risks......Page 170 6.3.7 ISDA 2009, Big Bang Protocol, Small Bang Protocol and new trading conventions......Page 172 6.4 Estimating default probability......Page 173 6.4.2 Historical estimation......Page 174 6.4.3 Equity-based approaches......Page 177 6.4.4 Market-implied default probabilities......Page 179 6.5.1 CDS index products......Page 181 6.5.2 Index tranches......Page 182 6.5.3 Super senior risk......Page 185 6.5.4 Collateralised debt obligations......Page 186 6.5.5 CDO investors......Page 187 6.5.7 Summary......Page 188 Appendix 6.B Pricing formulas for CDSs and risky bonds......Page 189 Appendix 6.C Pricing of index tranches......Page 192 7 Pricing Counterparty Credit Risk, I......Page 193 7.1.1 Motivation......Page 194 7.1.3 Credit value adjustment (unilateral)......Page 195 7.1.4 Practical CVA formula (no wrong-way risk)......Page 196 7.1.5 CVA as a spread......Page 197 7.1.7 How to calculate the EE for CVA......Page 200 7.2.1 CVA formula with collateral......Page 201 7.2.2 CVA formula with netting......Page 202 7.2.4 Marginal CVA......Page 204 7.2.5 Exotic products......Page 206 7.3.1 Background......Page 207 7.3.2 Bilateral CVA......Page 208 7.3.3 Example......Page 209 7.3.4 BCVA formula from credit spread......Page 211 7.3.5 BCVA or CVA?......Page 212 7.3.6 BCVA and break clauses......Page 214 7.3.7 BCVA and unwinding trades......Page 215 7.3.8 Walkaway features......Page 216 7.4 Summary......Page 217 Appendix 7.A Deriving the equation for credit value adjustment (CVA)......Page 218 Appendix 7.B Approximation to the CVA formula in the case of no wrong-way risk......Page 220 Appendix 7.D Specific approximations to the CVA formula for individual instruments......Page 221 Appendix 7.F Deriving the equation for bilateral credit value adjustment (BCVA)......Page 223 Appendix 7.G Approximation linking CVA formula to credit spreads for bilateral CVA......Page 225 Appendix 7.H Deriving the equation for BCVA under the assumption of a bilateral walkaway clause......Page 226 8.2 Wrong-way risk......Page 229 8.2.2 Right-way risk......Page 231 8.2.3 Examples of wrong-way risk trades......Page 232 8.2.4 Wrong-way risk and CVA......Page 233 8.3.2 Simple example......Page 234 8.3.3 Forward trade example......Page 235 8.3.5 Comparison of wrong-way risk approaches......Page 238 8.3.6 Risky option position......Page 239 8.3.7 Wrong-way risk and bilateral counterparty risk......Page 242 8.4.1 CDS payoff under counterparty default......Page 243 8.4.2 Quantifying CVA for a CDS......Page 244 8.4.3 Buying CDS protection......Page 245 8.4.4 Selling CDS protection......Page 247 8.5.1 Overview......Page 248 8.5.2 Credit indices......Page 249 8.5.3 Index tranches......Page 250 8.5.4 Super senior tranches......Page 251 8.5.5 Counterparty risk distribution across capital structure......Page 252 8.5.6 Impact of upfront tranche payments......Page 254 8.6.2 TRS transactions......Page 255 8.6.4 Converting counterparty risk to gap risk......Page 256 8.7.1 The leveraged super senior (LSS) trade......Page 258 8.7.2 Monolines......Page 261 8.7.3 Credit derivatives products companies (CDPCs)......Page 262 8.7.4 The value of protection purchased from monolines and CDPCs......Page 263 8.8 Summary......Page 264 Appendix 8.A Computing the EE of a typical forward exposure with correlation to a time of default......Page 265 Appendix 8.C Formula for pricing a CDS contract with counterparty risk......Page 266 Appendix 8.D Pricing of a leveraged super senior tranche......Page 268 9.1 Introduction......Page 269 9.2 Hedging and pricing......Page 270 9.3 Hedging a risky derivative position......Page 271 9.4 Traditional hedging of bonds, loans and repos......Page 272 9.5 Risk-neutral or real parameters?......Page 274 9.5.1 Futures prices and future spot prices......Page 275 9.5.2 Drift......Page 276 9.5.3 Volatility......Page 278 9.6 Components of CVA......Page 279 9.7 Recovery risk......Page 280 9.7.1 Basis risk......Page 281 9.7.3 Recovery swaps......Page 282 9.8.1 Static CDS hedging of exposures......Page 283 9.8.2 Contingent credit default swaps (CCDSs)......Page 284 9.9.1 Credit delta......Page 286 9.9.2 Gamma......Page 287 9.9.3 Jump-to-default risk......Page 288 9.10.1 Hedging spot rates......Page 290 9.10.2 Spot rates and drift......Page 292 9.10.3 Volatility......Page 293 9.11.1 Cross-gamma and wrong-way risk......Page 296 9.11.3 Monolines......Page 297 9.11.4 Hedging bilateral counterparty risk......Page 299 9.11.5 Impact of collateralisation on hedging......Page 301 9.12 Aggregation of sensitivities......Page 303 9.13 Summary......Page 304 Appendix 9.A Example of calculation of CVA Greeks......Page 305 10.1 Introduction......Page 307 10.2.1 Double-default approach......Page 308 10.2.2 Merton-style approach......Page 309 10.2.4 Impact on CCDS......Page 310 10.2.6 Impact of random exposure......Page 312 10.3 Credit portfolio losses......Page 313 10.3.1 Loss distributions and unexpected loss......Page 315 10.3.2 Impact of correlation......Page 316 10.4 The impact of stochastic exposure......Page 317 10.4.1 Impact of random exposure on unexpected loss......Page 318 10.4.2 The alpha factor......Page 319 10.4.3 Example of alpha correction......Page 321 10.5 Special cases of alpha......Page 322 10.5.2 Asymmetric exposure......Page 323 10.5.3 Wrong-way risk......Page 324 10.5.4 What is the correct value of alpha?......Page 326 10.6.2 Modelling credit migrations......Page 327 10.6.3 Marking-to-market loans......Page 328 10.6.5 Example......Page 329 10.7 Summary......Page 330 Appendix 10.A Credit portfolio model......Page 331 Appendix 10.B Simple treatment of wrong-way risk......Page 333 11.1 Introduction......Page 335 11.2 The birth of Basel II......Page 336 11.3.2 The advanced IRB approach......Page 337 11.3.3 Asset correlation......Page 338 11.4 Exposure at default and Basel II......Page 339 11.4.1 Current exposure method......Page 340 11.4.2 Standardised method......Page 341 11.4.3 Treatment of repo-style transactions......Page 342 11.5.2 Effective maturity......Page 345 11.5.3 Exposure at default......Page 346 11.5.4 Defining alpha......Page 347 11.5.5 Effective EPE for collateralised counterparties......Page 348 11.6.1 Background......Page 349 11.6.3 Double-default adjustment factor......Page 350 11.6.4 Accounting for double-default for derivatives......Page 352 11.7 Summary......Page 353 Appendix 11.A Effective remaining maturity......Page 354 Appendix 11.C Netting and collateral treatment under the current exposure method (CEM) of Basel II......Page 355 Appendix 11.D Definition of effective EPE......Page 356 Appendix 11.E Double-default treatment of hedged exposures in Basel II......Page 357 12.2.1 Components......Page 359 12.2.3 Responsibilities......Page 361 12.2.5 Mechanics of pricing......Page 362 12.2.7 Technology aspects......Page 363 12.3.1 Background......Page 365 12.3.2 Insurance approach......Page 366 12.3.3 Trading desk approach......Page 368 12.4.1 Real or risk-neutral?......Page 369 12.4.3 Drift, volatility and correlations......Page 370 12.5 How to charge for counterparty risk......Page 371 12.5.3 Pricing incorporating risk mitigants......Page 372 12.5.4 Allocation of CVA......Page 373 12.6 Summary......Page 375 13.1 The triple-A counterparty......Page 377 13.1.2 Derivatives product companies......Page 378 13.1.3 Monolines......Page 379 13.1.4 Credit derivatives products companies......Page 381 13.2.2 Rating agencies and triple-A entities......Page 382 13.2.3 Credit insurer simple example......Page 383 13.2.4 Suspension modes, downgrades and death spirals......Page 386 13.2.5 Termination mode and run-off......Page 387 13.2.6 The random leverage effect......Page 389 13.2.7 The future for credit insurers......Page 390 Appendix 13.B The valuation of credit insurer purchased protection......Page 391 14.1.1 Background......Page 395 14.1.2 Systemic risk in the derivatives markets......Page 396 14.1.3 Historical background to CCPs......Page 397 14.1.4 Bilateral netting versus centralised clearing......Page 398 14.1.5 Novation......Page 399 14.1.7 Impact of default of a CCP member......Page 400 14.1.8 Initial margin......Page 401 14.2 The viability of centralised clearing......Page 403 14.2.1 The advantage of centralised clearing......Page 404 14.2.3 Risk homogeneity and asymmetric information......Page 405 14.2.4 Competition......Page 406 14.2.5 Market coverage of a CCP......Page 407 14.2.6 Central counterparties and credit derivatives......Page 410 14.2.7 Under what circumstances will a CCP work?......Page 411 14.3 Conclusions......Page 412 15.1 A counterparty risk revolution?......Page 415 15.3 Collateral management......Page 416 15.5 Credit value adjustment (CVA)......Page 417 15.8 Central counterparties......Page 418 15.9 The overall challenge......Page 419 Glossary......Page 421 References......Page 431 Index......Page 437