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| Bielecki T.R., Rutkowski M. — Credit Risk: Modeling, Valuation and Hedging |
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| Предметный указатель |
Assumption, (A.1)—(A.6) 40—41
Assumption, (D) 239
Assumption, (J) 297
Assumption, (LR) 452
Assumption, (S.1)—(S.3) 470
Bankruptcy cost 77 84 88
Bankruptcy, endogenous 6
Bankruptcy, exogenous 6
Bankruptcy, optimality 83 84 88
Barrier constant 89 96
Barrier default triggering 6 32 41 65 80 85—87 90 97
Bond consol 50
Bond convertible 113
Bond coupon 21 24 35 50 415
Bond default-free (Treasury) 4 44 49 51 387
Bond defaultable (corporate) 4
Bond zero-coupon 47 48 53 62 73 91 99 104 110 232—234 247 259 355 364 372 387 390 397 412
Brady bonds see “Sovereign debt”
BSDE (backward stochastic diiferen tial equation) 244
CAP 455—457
Cap valuation formula 457
Cap-floor parity 457
Caplet 455
Ceiling rate agreement “see cap”
Claim attainable 35 45 247 464
Claim defaultable 33 35 222
Claim promised 33 41 222
Claim vulnerable 12
Collateral 22
Collateralized bond obligation 379
Compensator of a Poisson process 187
Compensator of a random time 140
Compensator of an increasing process 140 169
Condition (B.1)—(B.2) 316
Condition (BR.1)—(BR.10) 405—417
Condition (C.1) 268
Condition (C.2) 289
Condition (D.1)—(D.2) 371
Condition (F.1) 165
Condition (F.1a) 166
Condition (F.2) 166
Condition (G.1)—(G.3) 141—146
Condition (HJM.1)—(HJM.9) 386—404
Condition (JLT.1)—(JLT.7) 354—357
Condition (JLT.5c)—(JLT.7c) 362—363
Condition (K) 367
Condition (L.1)—(L.5) 374—375
Condition (M.1)—(M.2) 166
Condition (M.2a) 166
Condition (M.2b)—(M.2c) 167
Conditional expected recovery rate upon default 47
Conditional expected writedown rate 47
Conditional expected writedown rate upon default 47
Conditional independence of  -fields 166
Conditional independence of random times 268
Conditional Poisson process 193
Contingent claim see “Claim”
Counterparty risk 3
Counterparty risk, bilateral 13
Counterparty risk, unilateral 15
Coupon process 458
Cox process see “Process”
CRA (ceiling rate agreement) see “Cap”
Credit agreement, default-free 14
Credit agreement, defaultable 15
Credit default option 18 421
Credit default swap 18 421
Credit derivative 16—17
Credit derivative basket 266
Credit event 26
Credit linked note 22
Credit migration 28
Credit migration process 356 362 371 407
Credit rating (class, grade) 7 352 356 367 371 405
Credit risk 3
Credit risk, bilateral 3
Credit risk, counterparty 3
Credit risk, reference 3
Credit risk, unilateral 3
Credit spread 7 9 49 56
Credit spread forward 25
Credit spread model 264
Credit spread option 25
Credit spread swap 25
Credit swap 24
Cross default 11
Debt corporate, Merton's model 51
Debt service 88
Debt sovereign 11
Debt structure 86
Debt, protected 86
Debt, unprotected 85
Default correlation 11 114 284 416
Default distance-to 56 57
Default infectious 294
Default put 18
Default put, digital 236 267
Default swap 18 24
Default swap basket 281
Default time 26 222
Default time canonical construction 227
Defaultable bond see “Bond”
Defaultable claim see “Claim”
Defaultable interest rate see “Interest rate”
Defaultable martingale measure see “Martingale measure”
Defaultable swap see “Swap”
Distance-to-default 56 57 116
Dividend process 34 223 306 307 309 310 312 384
Dividend promised 33 35 222
Doleans' exponential 135 190 473
Doubly stochastic Poisson process 193
Econometric models 30 257—258
Exponential martingale 187
Filtration of default 123
Filtration, Brownian 33 56 222
Financial distress 7 56
First passage time 66—70
First-to-default contract 24 274
First-to-default swap 24 278
FLOOR 455
Forward martingale measure 49; see “Martingale measure”
Forward rate instantaneous defaultable 49 387 406
Forward rate instantaneous risk-free 49 386
Forward rate LIBOR 425
Forward rate swap 425
Forward survival process see “Process”
FRA (forward rate agreement) 424
Fractional recovery of market value 5 243 404
Fractional recovery of par value 5 233 404
Fractional recovery of Treasury value 5 233 400
Frictionless market 51
Gains process 39 224
Gaussian bivariate distribution (law) 116
Gaussian HJM set-up 90 112
Gaussian probability distribution (law) 52
Hazard function 125 229
Hazard process 142 225 251
Hazard rate (stochastic intensity) 155 226
Hedging corporate bond 55
Hedging defaultable claims 246
Hybrid approach 259—263
Hybrid derivative 13
Intensity matrix 325
Intensity, deterministic 227 232
Intensity, martingale see “Martingale”
Intensity, stochastic see “Hazard”
Interest rate agreement default-free 14 424
| Interest rate agreement defaultable 15 426—432
Interest rate swap, default-free 15 425
Interest rate swap, defaultable, multi-period 441—450
Interest rate swap, defaultable, single-period 432
Interest rate, defaultable 426—450
Interest rate, deterministic model 51
Interest rate, stochastic model, CIR 96 103
Interest rate, stochastic model, HJM 90 386
Interest rate, stochastic model, Vasicek 48 98 104
IRA see “Interest rate agreement”
Kusuoka's example 209—218 295—296
LIBOR (London interbank offered rate) 424—425
Liquidity risk 30 256
Market price of credit risk 418
Market price of interest rate risk 418
Markov chain conditional continuous-time 340
Markov chain conditional discrete-time 322
Markov chain continuous-time 324
Markov chain discrete-time 313
Markov chain discrete-time, embedded 329
Martingale associated with Poisson process 187
Martingale associated with transitions (migrations) 318
Martingale associated with Wiener process 188
Martingale hazard process 165
Martingale hypotheses 166 242
Martingale intensity 165 239
Martingale invariance property 166 242
Martingale measure, defaultable 391 399
Martingale measure, forward 48 90 99 100 108 389 399
Martingale measure, spot 38 41 48 222 246 389
Martingale representation theorem 131 156 178
Migration intensity, real-world 420
Migration intensity, risk-neutral 407
Migration process see “Process”
Model of credit migrations, Bielecki and Rutkowski 406
Model of credit migrations, Jarrow, Lando and Turnbull 354
Model of credit migrations, Kijima and Komoribayashi 367
Model of credit migrations, Lando 374
Model of credit migrations, Thomas, Allen and Morkel — Kings bury 371
Model of credit spreads, Das 264
Model of credit spreads, Nielsen and Ronn 264
Model of defaultable rates, Lotz and Schloegl 465
Model of defaultable rates, Schoenbucher 469
Model, hybrid, Madan and Unal 259
Model, reduced-form, Duffie and Singleton 255
Model, reduced-form, Jarrow and Turnbull 354
Model, reduced-form, Lando 253
Model, reduced-form,Jarrow and Yu 296
Model, structural, Black and Cox 71
Model, structural, Brennan and Schwartz 113
Model, structural, Cathart and El-Jahel 103
Model, structural, Kim, Ramaswamy and Sundare san 96
Model, structural, Leland 84
Model, structural, Leland and Toft 86
Model, structural, Longstaff and Schwartz 98
Model, structural, Merton 51
Model, structural, Saa-Requejo and Santa-Clara 107
Model, structural, Zhou 60
Model, structural,Briys and de Varenne 104
Note, credit-linked 22
Note, fixed-coupon 9
Note, floating-rate 9
Optimal capital structure 82
Option, call (put) 52
Option, credit default 18
Option, vulnerable 12
PDE (partial differential equation), Black — Scholes 46
PDE (partial differential equation), fundamental 45 112
PDE (partial differential equation), pricing 72 97 99 259
Poisson probability distribution (law) 186
Poisson process 60 186
Poisson process, compensated 187
Poisson, stopped 138 150 152 161
Poisson, survival 225 251
Predictable covariation 111 152
Priority rule 77 260
Process counting 347
Process, Cox 195 253
Process, forward survival 399
Process, marked point 347
Process, migration 356 362 371 407
Process, Poisson, compensated 187
Process, Poisson, conditional 193
Process, Poisson, doubly stochastic 193
Process, Poisson, marked 60
Process, Poisson, time-homogeneous 186
Protective covenant see “Safety covenant”
Put-call parity 52
Put-to-default 52
Quadratic covariation 152 154 158
Radon — Nikodym density 48 63 109 133 190 196 203 335 471
Random times, conditionally independent 268—274
Random times, ordered 265
Recovery at default 5 34 36 222 233
Recovery at maturity 5 34 36
Recovery claim 5 33 222
Recovery payoff 5 33 47 65 222 231 233 245 266
Recovery payoff, non-random 275 277—279
recovery process 5 33 222 245 375 433 440 449 467
Recovery process terminal 403 404 414 415
Recovery profile 413
Recovery rate 5 26 47 49 61 243 405
Recovery rule (scheme) 5 34 35 41 236 252 413
Recovery rule (scheme), endogenous 243
Recovery rule (scheme), multiple ratings 414
Recovery rule (scheme), single rating 403
Safety covenant 6 71
savings account 34 37 180 222 389
Savings account, default-risk-adjusted 231 237 240 254
Seniority rule see “Priority rule”
Sovereign debt 11
Spot martingale measure see “Martingale measure”
State variable 88 195 229 253 256
Stochastic exponential see “Doleans' exponential”
Stopping time 33 68 141 155 169 173 330
Stopping time, predictable 33 56 182 221
Stopping time, totally inaccessible 169 182 221
Strict priority rule 106
Swap asset 24
Swap interest rate, default-free 15 458
Swap interest rate, defaultable 13 432
Swap option see “Swaption”
Swap spot rate, default-free 15 425
Swap spot rate, defaultable 15 427
Swaption 462
Syndicated bank loan 11
Tax benefit 84
Term structure of credit spreads 7 56 106 110 364
Term structure, defaultable 4 387
Terminal recovery process see “Recovery process”
Threshold process see “Barrier”
Total rate of return swap 21 421
Total value of a firm 85
Total value of firm's assets see “Value of a firm”
Trading strategy, admissible 38 224
Trading strategy, buy-and-hold 37
Trading strategy, replicating 55
Trading strategy, self-financing 37 45 55 224
TROR (TRS) see “Total rate of return swap”
Value of a firm 32 33 51 82 84
Value, pre-default 36 232 241 387 406
Value, process 35
Value, process, ex-dividend 38 223
Value, process, integral representation 230
Vulnerable claim see “Claim”
Wealth process 37 224
Writedown rate 47 48 55 61
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