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| Rebonato R. — Interest-rate option models : understanding, analysing and using models for exotic interest-rate options |
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| Предметный указатель |
(State/price) tableau 492
Accrual notes 372
Adapted process 457
Admissible strategies 495 (see also trading strategy)
Affine models 285 413-22
Affine models, definition 413-14
Affine models, time-homogeneous 414-18
Affine models, time-inhomogeneous 418-20
Algebra 450
American (Bermudan) swaptions 14 15 36-40 227-30 431 432
Antithetic technique 226-7
Arbitrage 6 74 136
Arbitrage, definition 496
Arbitrage-free log-normal short-rate, calibration and parametrisation 361-4
Arbitrage-free log-normal short-rate, computational results 364-7
Arbitrage-free log-normal short-rate, implementation and numerical issues 358-61
Arbitrage-free log-normal short-rate, model description 355 8
Arbitrage-free log-normal short-rate, two-factor models 353-69
Arrears, LIBOR in 176-9
Arrow - Debreu prices 197 199 498 499 500-7
Attainable (contingent) claim 503
Average volatilities 76 77-80 275
Backward induction 194-7 429
Bermudan swaptions see American swaptions
Black and Scholes approach 157 162 247 256
Black Derman and Toy model 259-79 435
Black Derman and Toy model, analytic characterisation 260-2
Black Derman and Toy model, calibration 270-9
Black Derman and Toy model, calibration to caplets 272-3 274-5
Black Derman and Toy model, calibration to FRAs 271-2
Black Derman and Toy model, calibration to swaptions 273-4
Black Derman and Toy model, compared with HJM 389
Black Derman and Toy model, derivatives 268-70
Black Derman and Toy model, equivalence with generalized HW model 283-4
Black Derman and Toy model, realism 262-8
Black Derman and Toy model, time-dependence of short rate volatility 261 275-7
Black Derman and Toy model, two-factor models 441-3
Black Derman and Toy model, unconditional variance of short rate, continuous-time equivalent 440-1
Black Derman and Toy model, unconditional variance of short rate, discrete case 437-40
Black formula, applied to caps 16 18 91-2 175
Black formula, applied to European swaptions 18
Black formula, applied to floors 17
Black formula, for bond options 108
Black formula, for captions 47 78
Black formula, inverse 19
Black formula, links with Feynmann - Kac theorem 108
Black formula, perfect 76-7
Black formula, term 85-8
Black model caplets 237
Black model derivatives compared with BDT 268-70
Black model distributional assumptions compared with BDT 275-8
Black model in LS 323-5
Black model prices compared with HW 287 295-301
Black model volatilities 74 79-80 237 238
Bond options, CIR 246-9
Bond options, hedging, with underlying forward contract 106-9
Bond options, HW 288-9
Bond options, LS 325 7
Bond options, path-dependent 109-15
Bond pricing 19-20 21-7
Bond pricing, Brace - Gatarek - Musiela/Jamshidian model 100 183 184 393-409
Bond pricing, choice of pricing framework 402-6
Bond pricing, discretely-compounded money-market, account forward rates 395-9
Bond pricing, discretely-compounded money-market, swap rates 399-402
Bond pricing, observable and unobservable state variables 393-5
Branching 290-2
Brennan and Schwartz model 70 84 341-52 372
Brennan and Schwartz model, modified 71
Brownian motion 152 153 190 406 471-4
BS 342-5 347-9
BS, CIR 244
Bushy trees 137 216 458
Calibration, arbitrage-free log-normal short-rate two-factor models 361-4
Calibration, BDT 270-9
Calibration, CIR 249-51
Calibration, HW 295-301 306-8 337-9
Calibration, LS 327-8 332-9
Calibration, to cap prices of models 435-45
Callable bond see American swaptions
Cap(let), calibration to BDT 272-3 274-5
Cap(let), calibration to Black formula 15 18 47 78
Cap(let), calibration to HW 295-301 306-8
Cap(let), definition 16
Cap(let), prices 435-45
Cap(let), prices, affine models 422
Cap(let), prices, and unconditional forward rate variance 237
Cap(let), prices, BDT 271
Cap(let), prices, BGM/J 398
Cap(let), prices, Black 16
Cap(let), prices, HW 296-301 306 308
Cap(let), ratchet see one-way-floaters
Cap(let), valuation 16
Cap(let), volatility 76 77
Captions 47-50
Chooser accrual notes 372
Complement, definition 448
Complete market, definition 503
Conditional expectation 463-6
Conditional present value 496 500
Consol bond 355
Consol bond, CIR 243 244
Consol rate see consol yield
Consol yield 356-8
Constant Maturity Swaps (CMS) 30 36
Constant Maturity Swaps (CMS), options on 15
Contingent claim 6 120-1
Contingent claim, attainable 502-3
Contingent claim, brought-back 139
Contingent claim, definition 502
Contingent claim, evaluation in a multi-period setting 136-8
Contingent claim, evaluation of fair price, marked price of risk 125-8
Contingent claim, evaluation of fair price, naive expectation 123-5
Contingent claim, evaluation of fair price, replication strategy 121-3
Contingent claim, evaluation of fair price, risk-neutral valuation 129-30
Contingent value 496
Contravariate technique 222-3
Correlation, between forwards 59 60
Correlation, between forwards and short rate 323-5
Correlation, in HWE 304
Correlation, in low-dimensionality models 304
Correlation, in LS 323-5
Correlation, perfect 76-7
Correlation, term 85-8
Covariance (see also correlation)
Covariance between factors 55-6
Covariance matrix 18-19 52-6
Cox - Ingersoll - Ross model, analytic properties 243-5
Cox - Ingersoll - Ross model, bond options 246-9
Cox - Ingersoll - Ross model, derivation 239-42
Cox - Ingersoll - Ross model, empirical results 251 7
Cox - Ingersoll - Ross model, parametrisation 249-51
Cross-sectional estimation, CIR 255
Delta derivative in BDT 270
Derivatives in BDT 268-70
Deterministic economy 162-5
Diffusion equation see partial differential equations: parabolic dimensionality of interest-rate models 72
Discount bonds, as numeraire 170-4
Discount bonds, definition 5
Discount bonds, future volatilities and 252
Discount bonds, relationship with forward rates 19
discount factor 495
Discount function 5 (see also yield curve)
Discount function, analytic properties, CIR 243-5
Discount function, analytic properties, in HW 284-7
Discount function, analytic properties, in LS 320-1
Discount function, definition 20
Discount function, determination, bond-linear models case 21-5
Discount function, determination, bond-non-linear models case 25-7
Discount function, determination, HJM 380-4
Discount function, determination, LIBOR curve case 27-8
| Discount function, from spanning forward or swap rates 14-15
Eigenvalues of covariance matrix 57 64
Eigenvectors of covariance matrix 57 6
Elementary event 449
Equilibrium economy 249
Equilibrium economy in LS 314-15
Equilibrium swap rate 10-12
EQUIVALENCE 452
Equivalent probability measure see Probability Measure
European swaption, definition 17
European swaption, pricing instaneous volatilities with 80-3
European swaption, valuation 17-18
Event 449 452
Evolutionary approach 73
Exercise boundary function 40
Exotic options 3-5
Expectation Hypothesis 165
Explicit Finite Differences 208-12
Extended CIR model 283
Extended Vasicek (EXV) model 282 283 310 311
Face value, definition 5
Factors 55-8 (see also principal components analysis)
Feynman - Kac theorem 108 246 284 486
Field 450
Filtration 457
Finite differences 205-7
Finite differences, explicit 208-12
Finite differences, infinite 212-13
Fixed leg of swap 8
Fixed leg of swap in BDT 273
Flat-volatility assumption 75
Floating leg of swap 9 10 13
Floating leg of swap in BDT 273 274
Floor(let), definition 16
Floor(let), ratchet see one-way-floaters
Floor(let), valuation 16-17
Fokker - Plank equations 205 219
Forward induction 197-9
Forward rates, BGM/J 395-8
Forward rates, definition 5-8
Forward rates, degree of correlation between spot rate and 59 60
Forward rates, degree of correlation for changes 59
Forward rates, discrete, continuously compounded 7
Forward rates, discrete, simply compounded 7
Forward rates, instantaneous 7
Forward rates, link with discount function 24
Forward rates, spanning 14-15 183-4
Forward rates, with affine models 416-18
Forward-neutral measure 142
Fourier series 65-6 70
FRAs, and futures 27
FRAs, calibration to BDT 271-2
FRAs, set in arrears 176-7
FRAs, valuation of 8-14
Fubini's theorem 385 387 393
Fundamental approach to calibration see historical approach to calibration
Gamma derivative 270
Girsanov's theorem 113 136 153-5 175 195 486-90
Green's function 169 195 197-8 199 293-5 498
Gross redemption yield 21
Heath Jarrow and Morton model 84 98 184 215 220 371-90
Heath Jarrow and Morton model, compared with BDT 389
Heath Jarrow and Morton model, compared with Extended Vasicek 389
Heath Jarrow and Morton model, constraints on discount bond volatilities 380-4
Heath Jarrow and Morton model, log-normal bond prices 378-80
Heath Jarrow and Morton model, short rate process 384-9
Hedge ratio in BDT 269
Hedge-payoff mismatch instruments 29-30
Hedging, bond option with underlying forward contract 106-9
Hedging, path-dependent bond option with forward contracts 109-15
Historical approach (to calibration), CIR 249
Historical approach (to calibration), LS 318 337-9
Ho and Lee 241 265 316-17 417 427
Hogan instability 350
Hopscotch method 212
Hull and White approach 44 84 239 281-312 417
Hull and White approach, calibration, one-factor model 295-301
Hull and White approach, calibration, two-factor model 306-8
Hull and White approach, constructing for constant reversion speed and volatility 289-95
Hull and White approach, exact fitting to term structure of volatilities 288-9
Hull and White approach, Green's functions 293-5
Hull and White approach, normal-rates see Extended Vasicek (EXV) model
Hull and White approach, numerical implementation 308-11
Hull and White approach, one-factor version 283-7
Hull and White approach, two-factor version 301-5
Implied approach (to calibration) LS 332-7
Impossible event 449
Incompatible set, definition 448
Independence 461
Independent random variables 463
Index rate, definition 41
Indexed - Principal Swaps (IPSs) 30
Information structure 457
Inhomogeneity see time-inhomogeneity
Intersection, definition 447
Ito integral, elementary 216 217
Ito integral, elementary of adapted process 480
Ito's lemma 110 184 208 240 247 260 481-5
Knock-out caps 30
Kolmogorov equations 120 205 219
Lattice models, backward induction 194-7
Lattice models, forward induction 197-9
Lattice models, justification 189-94
LIBOR curve, discount function determination by 27-8
LIBOR-in-arrears swaps 30-6 176-9
LIBOR-in-arrears swaps, definition 30
London Inter-Bank Offered Rates see LIBOR
Longstaff and Schwartz model 70 248 253 313-40 422
Longstaff and Schwartz model, calibration 327-8
Longstaff and Schwartz model, calibration, using historical approach 337-9
Longstaff and Schwartz model, correlation between rates 323-5
Longstaff and Schwartz model, economy 314-15
Longstaff and Schwartz model, equilibrium term structure 320-1
Longstaff and Schwartz model, fitting yield curve using implied approach 328-32
Longstaff and Schwartz model, option pricing 325-7
Longstaff and Schwartz model, term structure of volatilities 321-2
Market price of long yield risk 342-5
Market price of risk 159-60
Markovian models, choice of model 429-34
Markovian models, condition for Markovian rate process 425-8
Markovian models, definition of Markovian rate processes 423-5
Martingale Variance Reduction (MVR) approach 223-6
Martingales 143 474-7
Martingales, approach 73 74
Martingales, representation theorem 475-6
Martingales, super- and sub 474
Martingales, transform 475
Mean reversion, contrasted with time-dependent volatility 239 440
Mean reversion, in BDT 261
Mean reversion, in HW 282 283 292
Measurable space 451
Measurable variables 455
Measure see probability measure
Minimal geld 451
Money-market account 373
Money-market account, and drift of forward rates 376
Money-market account, as numeraire 165-70
Money-market account, BGM/J 295-8 399-40
Monte Carlo method 215-30
Monte Carlo method, American options 40 227-30
Monte Carlo method, in evaluation of trigger swaps 44
Monte Carlo method, variance-reduction techniques 222-7
Newton - Raphson yield 363-4 390
Newton - Raphson yield, gross redemption 20
Newton - Raphson yield, of a discount bond 6
No-arbitrage BS model 342-5
No-arbitrage Martingale approach 160-2
No-arbitrage Vasicek approach 157-60
No-arbitrage, conditions of 157-84
Non - Markovian models (see also Markovian models)
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