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Rebonato R. — Interest-rate option models : understanding, analysing and using models for exotic interest-rate options
Rebonato R. — Interest-rate option models : understanding, analysing and using models for exotic interest-rate options

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Название: Interest-rate option models : understanding, analysing and using models for exotic interest-rate options

Автор: Rebonato R.

Аннотация:

The modelling of exotic interest-rate options is such an important and fast-moving area, that the updating of the extremely successful first edition has been eagerly awaited. This edition re-focuses the assessment of various models presented in the first edition, in light of the new developments of modelling imperfect correlation between financial quantities. It also presents a substantial new chapter devoted to this revolutionary modelling method. In this second edition, readers will also find important new data dealing with the securities market and the probabilistic/stochastic calculus tools. Other changes include: a new chapter on the issues arising in the pricing of several classes of exotic interest-rate instruments; and insights from the BDT and the Brennan and Schwartz approaches which can be combined into a new class of "generalised models". Further details can be found on the links between mean-reversion and calibration for the important classes of models.

Dr Riccardo Rebonato is Director and Head of Research at Barclays Capital. He is responsible for the modelling, trading and risk management of the European exotic interest-rate products. He holds Doctorates in Nuclear Engineering and Science of Materials/Solid State Physics. Before moving into investment banking he was Research Fellow in Physics at Corpus Christi College (Oxford). He has published papers in several academic journals in finance, and is a regular speaker at conferences worldwide.


Язык: en

Рубрика: Математика/Вероятность/Стохастические методы в финансах/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1998

Количество страниц: 521

Добавлена в каталог: 12.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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