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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 |
Non - Markovian models, choice of model 429-34
Non - Markovian models, on recombining trees 428-9
Notional value, definition 5
Numeraire asset 495
Numeraire discount bonds 170-4
Numeraire money market account 165-70
Numeraire switching under different measures 144-50
One-factor models, main desired features 233-4
One-way-floaters 44-7
Options on bonds see bond options
Par coupon rates, definition 5-8
Par coupon, definition 13
Partial differential equations, parabolic 201-4 485-6
Partial differential equations, stochastic 481-5
Partial differentiation approach (PDE) 106-9 157 201-13
Partial differentiation approach (PDE) for generic security 284
Partial differentiation approach (PDE), BS model 345-6
Partial differentiation approach (PDE), finite-differences approximations to 205-7
Partial differentiation approach (PDE), HW model 284
Partial differentiation approach (PDE), LS model 315-16
Partial differentiation approach (PDE), underlying parabolic equation 201-4
Partition 453
Payer swaption 36
Power set 450
Predictable process 457
Present value 496
Previsible process 457
Price vector 492
Pricing framework 134-6
Principal components analysis 58-61 70 73 84 325
Principal value, definition 5
Probability measure 142 451
Probability space 451
Proper subset, definition 448
Pseudo-probabilities 130-4 141-2 143 144-6
Put/call parity 269
Radon - Nikodym derivative 147 148 486-90
Random experiment 449
Random variables 455
Random variables, independent 463
Random walk 152 (see also Brownian motion)
Rates, definition 8
Rates, statistical analysis 51-63
Receiver swaption 36
Recombination of trees 425 431
Recombination of trees in CIR 253
Recombination of trees in HW 283 292
Recombination of trees with non - Markovian models 428-9
Relative prices 495
Reversion level in BS 345
Reversion speed (see also mean reversion)
Reversion speed in BS 345
Reversion speed in CIR 253 256
Reversion speed in HW 289-95
Riemann sum 217 480
Risk-neutral measure 142
Sample space 449
Self-financing strategy 139-41 494
Sensitivity of yields to short rate (BDT) 263-4
Set, definition 447
Short rate BS 347-9
Short rate in BDT 437-41
Short rate in HJM 384-9
Short rate in LS 319-22
Short rate, variance of 444-5
Spot rate (see also short rate state/security)
Spot rate, continuously compounded discrete, of maturity 6
Spot rate, definition 5-8
Spot rate, degree of correlation between instantaneous forward rate and 59 60
Stochastic differentiation 481-5 (see also Ito's lemma)
Stochastic differentiation, parabolic partial differential equations and 485-6
Stratonovich integral 217
Subset, definition 448
Sure event 449
Swap rates, BGM/J 399-402
Swap rates, definition 5-8
Swap rates, in BDT 274
| Swaps, fixed leg 8
Swaps, floating leg 8 9
Swaps, plain-vanilla, valuation of 8-14
Swaps, pricing in BDT 271
Swaptions (see also American swaptions; European swaptions)
Swaptions, calibration to BDT 273-4
Swaptions, pricing with Black 18
Swaptions, pricing with HW 304
Sydney - Opera - House effect 71 85 367
Term correlation 85-8
Term structure of interest rates, definition 20 (see also yield curve)
Term structure of volatility, affine models 415
Term structure of volatility, and future volatility of the short rate 428
Term structure of volatility, and volatility of discount bonds 428
Term structure of volatility, evolution over time 82 94-5
Term structure of volatility, in BDT 262 263
Term structure of volatility, in HW 288-9 302-4
Term structure of volatility, time-homogeneous 96-7
Time homogeneity 99 101
Time homogeneity, affine models 414-18
Time homogeneity, in HJM 385-6
Time inhomogeneity, affine models 418-20
Time stationarity see time homogeneity
Time-dependence of volatility in BDT 261 275-7
Time-dependence of volatility, contrasted with mean reversion 239 440
Tower Law 142-3 466
Trading horizon 491
Trading strategy 493
Trading strategy, self-financing 139-41 494
Tribe 450
Trigger swaps 30 41-4
Trinomial lattices, HW model 289-95
Two-factor interest-rate model 441-3
Two-factor interest-rate model, example 458-63
Unconditional present value 500
Union, definition 447
Unitary symmetric random walk 467-70
Vaillant brackets 179-84 395 400
Value rate, definition 41
Vasicek model criticism 241
Vasicek model derivation 239-42
Vasicek no-arbitrage condition see no-arbitrage
Volatility (see also term structure of volatility)
Volatility, average 76 77-80
Volatility, BDT 277-9
Volatility, cap 76 77
Volatility, flat-volatility assumption 75
Volatility, instantaneous 76 77-80
Volatility, instantaneous, flat 98-9
Volatility, instantaneous, identical 99-100
Volatility, instantaneous, of short rate, BDT 261 275-7
Volatility, instantaneous, of short rate, CIR 257
Volatility, instantaneous, of short rate, LS 314
Volatility, instantaneous, perfect correlation 76 77
Volatility, instantaneous, pricing European swaptions with 80-3
Volatility, instantaneous, time-homogeneity requirement 99 101
Volatility, of discount bonds 253
Volatility, of forward bond price 173
Volatility, swaption 76 77
Volatility, term decorrelation 83-91
Wealth in the LS economy 314-15
Wiener processes 205 436
Yield changes, predicted and experienced in BDT 264-8
Yield changes, predicted and experienced in LS 328-32
Yield curve in CIR 244-6 252
Yield curve, definition 20
Yield curve, effect of model dimensionality on option pricing 63-72
Yield curve, evolution of 51-63
Yield curve, in HJM 381-4
Yield curve, in LS 321-2 328-32
Yield curve, one-factor models 62-3 72
Yield curve, option pricing framework 72-4
Yield curve, sigmoid-like correlation structure 67-70
Yield curve, two-factor models 61-2 70 71
Yield of discount bonds (LS) 323-5 (see also spot rate)
Yield of T-maturity bond 203
Yield volatilities in LS 322-4
Zero-coupon bonds see discount bonds
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