Credit Derivatives : Trading, Investing,and Risk Management

Credit Derivatives......Page 4
Contents......Page 10
Preface......Page 18
Acknowledgements......Page 20
Disclaimer and Software Instructions......Page 22
Table of Spreadsheet Examples and Software......Page 26
PART I CREDIT BACKGROUND AND CREDIT DERIVATIVES......Page 28
1.1.2 BBA LIBOR and swaps......Page 30
1.1.3 Collateralised lending and repo......Page 31
1.1.4 Repo as a credit derivative......Page 32
1.3.1 Issue documents and default......Page 33
1.3.2 Claim amount......Page 34
1.3.3 The recovery process and recovery amount......Page 35
1.4 Valuation, yield and spread......Page 36
1.6 Marking to market, marking to model and reserves......Page 37
2.1.1 Ultimate recovery......Page 40
2.1.2 Market recovery......Page 41
2.1.3 Recovery rates and industry sector......Page 42
2.1.5 Modelling recovery rates......Page 43
2.3 Transition matrices......Page 45
2.4 ‘Measures’ and transition matrix-based pricing......Page 48
2.6 Adjusting transition matrices......Page 51
3.1.2 Hedging......Page 54
3.3 Maturity and z-spread......Page 55
3.4.1 Callable asset swaps......Page 57
3.5 A bond spread model......Page 58
4.2 The credit pyramid......Page 60
4.3 Survey and engineered spread data......Page 61
4.3.1 Survey data......Page 62
4.4 Spread and rating......Page 63
5.2 Collateralisation and netting......Page 66
5.4 Internal capital charge......Page 67
6.2 Distribution of forward values of a credit bond......Page 68
6.3 Correlation and the multi-factor Normal (Gaussian) distribution......Page 70
6.4 Correlation and the correlation matrix......Page 71
7.1.2 ‘Single Name’ credit derivatives......Page 74
7.1.4 Portfolio credit derivatives......Page 75
7.2 Market participants and market growth......Page 76
PART II CREDIT DEFAULT SWAPS AND OTHER SINGLE NAME PRODUCTS......Page 80
8.1.1 Contract description and example......Page 82
8.1.2 Market CDS quotes......Page 83
8.2.1 ISDA documentation and insurance contract differences......Page 84
8.2.2 Reference obligations and ‘Mark-it RED’......Page 87
8.3.2 Restructuring......Page 88
8.4 CDS applications and elementary strategies......Page 89
8.4.1 Single names......Page 90
8.4.3 Income generation......Page 91
8.4.4 Regulatory capital reduction......Page 92
8.6.1 Mechanics of transacting a CDS deal......Page 93
8.6.2 Trade Monitoring, credit events, unwinds......Page 94
8.6.3 CDS desk interactions and organisation......Page 95
Addendum: ISDA 2003 CDS Confirmation......Page 96
9.1 The fundamental credit arbitrage – repo cost......Page 106
9.2.1 Claim amount......Page 107
9.2.2 Recovery modelling......Page 108
9.2.3 Hazard (default) rate model......Page 109
9.2.4 Choice of hazard rate function/interpolation process......Page 110
9.3 Deterministic default rate model......Page 111
9.3.1 CDS valuation......Page 112
9.3.3 CDS under constant hazard rate......Page 114
9.3.6 Limiting cases of the bond price......Page 115
9.3.8 CDS and bond sensitivities......Page 116
9.4 Stochastic default rate model; hazard and pseudo-hazard rates......Page 117
9.5.1 Calibrating to CDS and to bonds......Page 120
9.5.3 Calibrating to bonds: multiple solutions for the hazard rate......Page 121
9.5.5 Implied hazard rate curve and no-arbitrage......Page 122
9.6.1 Survey data......Page 124
9.6.2 Data engineering......Page 126
9.7.2 Interest and hazard rate correlation......Page 127
9.7.3 Reference name and counterparty hazard rate correlation......Page 128
9.7.4 Interpolation assumptions, and the pseudo-hazard rate versus stochastic hazard rate......Page 129
9.8.1 Captured and hidden risks......Page 130
9.8.3 Reserves against implementation errors......Page 131
9.8.4 Model reserves......Page 132
10.1.1 Cross-currency default swap pricing and hedging......Page 134
10.1.2 Back-to-back trades, default event hedges and curve trades......Page 139
10.1.3 Hedging both credit event and spread risk simultaneously......Page 144
10.1.5 Trade level hedging and book basis hedging......Page 146
10.2.1 Default event hedging......Page 148
10.2.2 Spread hedging......Page 149
10.3 Hedge and credit event examples......Page 151
11.1 Bond versus CDS: liquidity......Page 156
11.2 Bond repo cost......Page 157
11.4 Bond price impact......Page 158
11.5 Embedded options in bonds......Page 159
11.6 Delivery option in CDS......Page 160
11.9 Embedded repo option......Page 161
11.10 Putting it all together......Page 163
12.1 Forward CDS......Page 164
12.2 Mark-to-market and back-to-back CDS......Page 165
12.3 Unwind calculation; off-market trade valuation and hedging......Page 166
12.4 ‘Double-trigger CDS’......Page 167
13.1 CLN set-up; counterparty or collateral risk......Page 170
13.4 Applications......Page 173
13.5.2 CLN pricing model......Page 174
13.6 Capital guaranteed note......Page 175
14.2.1 Simple pricing......Page 180
14.2.3 Valuation and hedging......Page 181
14.3 Trigger event differences......Page 182
15.1.1 Vanilla spread options and variations......Page 184
15.1.2 Related embedded products......Page 185
15.1.3 Bond price options......Page 186
15.2.1 Model approaches......Page 187
15.2.2 Hazard rate tree......Page 188
15.3 Sensitivities and hedging......Page 189
16.2 Applications......Page 190
16.3.1 Pricing and hedging......Page 191
16.3.2 Valuation......Page 192
17.1 Risk aggregation......Page 194
17.2 Credit VaR for CDS......Page 197
18.2 Valuation by Monte Carlo simulation......Page 198
18.3 Sensitivity......Page 201
PART III PORTFOLIO PRODUCTS......Page 204
19.1.1 First-to-default product definition and example......Page 206
19.1.2 Documentation and takeovers......Page 207
19.1.3 Second (and higher)-to-default......Page 208
19.2.3 Standard baskets......Page 209
19.3 Pricing: zero and 100% correlation......Page 210
19.3.1 Zero correlation case – exact pricing from the CDS model......Page 212
19.3.2 100% correlation: exact pricing......Page 216
20.1.1 Product definition......Page 220
20.1.2 Premium waterfall......Page 224
20.1.3 Documentation; CDO set-up......Page 225
20.1.4 CDO tranches; funded and unfunded tranches; ‘buying’ and ‘selling’......Page 226
20.1.6 Arbitrage CDOs......Page 227
20.2 Index portfolios and standard CDO structures......Page 228
20.2.1 Background and terminology......Page 229
20.2.3 Single tranche [0%, 100%] CDO products......Page 230
20.2.4 Standard tranched CDO structures: iTraxx and CDX......Page 232
20.2.5 Index options and modelling spread......Page 233
20.3.1 OC and IC tests; WARF; diversity score......Page 235
20.3.2 Cash and cashflow CDOs......Page 236
20.3.3 Cashflow waterfall......Page 238
20.3.4 Managed CDOs......Page 240
20.4 Tranche ratings and BET......Page 241
20.5 SPVs and CDOs......Page 244
20.6 Applications......Page 245
20.6.1 Balance sheet CDOs......Page 246
20.6.2 Diversification and risk reduction trades; a ‘credit bank’......Page 247
21.1.2 Intuitive understanding of default time correlation......Page 248
21.1.3 Spread implications of 100% default time correlation......Page 250
21.2 The normal copula......Page 251
21.3.1 N2D baskets......Page 252
21.3.2 CDO tranches......Page 253
21.3.4 Variance reduction techniques......Page 254
21.3.5 Complex CDO structures......Page 255
21.4 Valuation examples......Page 256
21.4.2 CDO pricing: change of correlation......Page 257
21.4.4 CDO pricing: change of underlying......Page 259
21.5.1 Dynamic hedging: spread risk......Page 261
21.5.2 Static hedging: default event risk......Page 268
21.5.3 Correlation risk......Page 270
21.5.5 Convexity risks......Page 271
21.6.1 Captured and hidden risks......Page 272
21.6.2 Spread models......Page 273
21.6.3 Reserves......Page 275
22 The Correlation Matrix......Page 278
22.1 Constraints: what makes a correlation matrix?......Page 279
22.2.1 Index CDO deals and implied correlation......Page 280
22.2.2 Base correlation......Page 282
22.2.3 Interpolating correlation......Page 283
22.3 Tag correlation and semi-closed form pricing......Page 284
22.4 Spread correlation......Page 285
22.5 Asset and equity correlation......Page 286
22.6.1 Pairwise estimation from historical data......Page 287
22.6.2 Factor analysis and correlation......Page 288
22.6.3 Impact on hedging of using historical or implied correlations......Page 290
23.1 Student’s t distribution......Page 292
23.2 Copulae in general......Page 293
23.3 Archimedean copulae: Clayton and Gumbel......Page 294
23.5 Model risk......Page 296
Addendum......Page 298
24.1 Static and dynamic hedges......Page 300
24.2 Correlation book management......Page 301
24.3 Credit VaR and counterparty VaR......Page 304
PART IV DEFAULT SWAPS INCLUDING COUNTERPARTY RISK......Page 306
25.1 Non-correlated counterparty......Page 308
25.2 100% correlation......Page 309
25.3 Correlated counterparty: pricing and hedging......Page 311
25.5 Collateralised deals and CDS book management......Page 312
26.2 Counterparty CDS (CCDS) book management......Page 316
27.1 Areas of development......Page 320
27.1.1 Market growth and investors......Page 321
27.2 Conclusion......Page 322
Appendix: iTraxx Indices......Page 324
References......Page 330
Index......Page 332