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Shreve S.E. — Stochastic Calculus for Finance 2
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Название: Stochastic Calculus for Finance 2Автор: Shreve S.E. Аннотация: Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Masters level students and researchers in mathematical finance and financial engineering will find this book useful. Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.
Язык: Рубрика: Экономика и финансы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 550Добавлена в каталог: 28.06.2006Операции: Положить на полку |
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1 52 4 8 20 531 52 50 Absolute continuity of probability measures 45 Adapted stochastic process 53 97 Additivity, countable 2 Additivity, finite 3 Affine yield 274 405 Almost everywhere 22 Almost everywhere, convergence 24 Almost surely 7 23 Almost surely, convergence 23 American options 339 American options, perpetual put 345 Arbitrage 230 Arbitrage, statistical 188 Arrival times 463 Asian option 278 320 Asian option, discretely sampled 329 Asian option, zero-strike call 336 atom 51 Augmentation of state 321 Backward equation (Kolmogorov) 291 Barrier options 299 Bermudan option 339 Black caplet formula 439 Black — Scholes — Merton, boundary conditions 158 Black — Scholes — Merton, formula 118 Black — Scholes — Merton, formula, for time-varying nonrandom interest rate 253 Black — Scholes — Merton, function 159 220 Black — Scholes — Merton, partial differential equation 157 Black — Scholes — Merton, put formula 164 Bootstrapping 403 Borel, 4 8 20 57 528 Borel, measurable function 21 Borel, set 4 7 Brace — Gatarek — Musiela model 405 see Brownian bridge, as conditioned Brownian motion 182 Brownian bridge, from 0 to 0 175 Brownian bridge, from a to b 176 Brownian bridge, maximum of 183 Brownian bridge, multidimensional distribution 178 Brownian motion 94 Brownian motion, correlated 197 199 200 Brownian motion, covariance 95 Brownian motion, filtration for 97 Brownian motion, fractional 188 Brownian motion, Markov property 107 Brownian motion, martingale property 98 Brownian motion, maximum to date 113 Brownian motion, maximum to date, with drift 295 Brownian motion, moment-generating function 96 Brownian motion, multidimensional 164 Brownian motion, other variations 117 Brownian motion, quadratic variation 102 Brownian motion, reflection principle 111 Brownian motion, relative to a filtration 473 Brownian motion, transition density 108 Brownian motion, transition density with drift 119 Brownian motion, uncorrelated dependent 204 Calibration 272 Call option, European 155 Cantor set 528 CAP see “Interest rate cup” Caplet see “Interest rate cuplet” Central limit theorem 89 Change of measure 32 Change of measure for Brownian motion 212 224 Change of measure for compound Poisson process 500 Change of measure for compound Poisson process and Brownian motion 503 Change of measure for exponential random variable 47 Change of measure for normal random variable 36 46 Change of measure for Poisson process 494 Change of numeraire, change in volatility caused by 400 Change of numeraire, portfolio under 398 Change of numeraire, to price Asian option 326 Chooser option 256 Coin-toss space 4 Complete model 223 231 Compound Poisson process 468 Compound Poisson process, compensated 470 Compound Poisson process, decomposition 471 Compound Poisson process, moment-generating function 470 Compound Poisson process, relative to a filtration 474 Conditional density 80 Conditional expectation 69 Conditional expectation, existence 533 Conditional expectation,independence 70 Conditional expectation,iterated conditioning 70 Conditional expectation,linearity 69 Conditional expectation,taking out what is known 70 Constant elasticity of variance 272 Continuation set 357 Convergence almost everywhere 24 Convergence almost surely 23 Correlated Brownian motions 197 199 200 Correlated stock prices 171 Correlation 62 Correlation, instantaneous 201 227 Correlation, under change of measure 257 Cost of carry 259 Countable additivity 2 527 Covariance 62 Covariance for Brownian motion 95 Cox — Ingersoll — Ross interest rate model 151 266 275 Cox — Ingersoll — Ross interest rate model, hitting zero 288 Cox — Ingersoll — Ross interest rate model, moment generating function for 286 Cox — Ingersoll — Ross interest rate model, solution of 285 Cox — Ingersoll — Ross interest rate model, two-factor 422 Cumulative distribution function (cdf) 10 Cumulative normal distribution 12 Delta 159 193 Delta, hedging rule 157 Delta, neutral 161 Delta, of an option 157 Delta, short 161 Density function 10 Density function, conditional 80 Density function, joint 57 Density function, marginal 58 80 Differential 215 Differential-difference equation 509 Diffusion 263 Discount process 227 272 Distribution, joint 57 Distribution, marginal 58 Distribution, measure 9 Dividend-paying stocks 234 Dividend-paying stocks, risk-neutral pricing formula for 236 Doleans — Dade exponential 491 Domestic risk-neutral measure 383 Dominated Convergence Theorem 27 Drift 263 Early exercise premium 339 Efficient market hypothesis 188 Equivalent probability measures 34 Euler method 267 European call 155 European put 163 Event 1 Exchange rate 382 Exchange rate, as dividend-paying asset 385 Exchange rate, forward 388 Exchange rate, paradox 387 Exchange rate, put-call duality 390 Exotic option 295 Expectation (expected value) 17 Expectation (expected value), computation of 27 31 Exponential martingale 109 Exponential random variable 462 Exponential random variable, memorylessness for 463 Feynman — Kac Theorems 268 269 Feynman — Kac Theorems, two-dimensional 286 Filtration for Brownian motion 51 Finite additivity 3 First passage time 110 First passage time, as a stopping time 341 First passage time, distribution 112 First passage time, Laplace transform for Brownian motion 119 122 First passage time, Laplace transform for Brownian motion with drift 346 First-order variation 99 Fokker — Planck equation 291 Foreign exchange model 381 Foreign risk-neutral measure 386 Forward equation (Kolmogorov) 291 Forward, contract 162 241 Forward, exchange rate 388 Forward, LIBOR 437 Forward, LIBOR models 405 Forward, measure 393 Forward, price 163 241 392 Forward, rate 405 424 Forward-futures spread 247 Fractional Brownian motion 188 Fundamental Theorems of Asset Pricing, First 231 Fundamental Theorems of Asset Pricing, Second 232 Futures price 244 Gamma 159 Gamma density 464 Gamma density, long 161 Garman — Kohlhagen formula 390 Gaussian process 172 Generalized geometric Brownian motion 147 191 Geometric Brownian motion 106 Geometric Brownian motion, generalized 148 191 Geometric Brownian motion, limit of binomial model 120 Geometric Brownian motion, maximum to date 334 335 Geometric Brownian motion, transition density 119 Geometric Poisson process 486 Girsanov’s Theorem, multi-dimensional 224 Girsanov’s Theorem, one-dimensional 212 Greeks 159 Heath — Jarrow — Morton model 404 Heath — Jarrow — Morton model, calibration of 432 Heath — Jarrow — Morton model, multifactor 458 Heath — Jarrow — Morton model, no-arbitrage condition 428 Heath — Jarrow — Morton model, under risk-neutral measure 429 Hedging a cash flow 256 Hedging equations 232 Heston stochastic volatility model 288 Hull — White interest rate model 265 274 Hull — White interest rate model, solution of 285 Implied volatility 271 Independence among sequence of 56 Independence among sequence of random variables 56 Independence between 54 Independence between normal random variables 61 Independence between random variable and 54 Independence between random variables 54 Independence between set and random variable 45 Independence between sets 54 Independence lemma 73 Indicator function 17 22 Indicator random variable 17 Instantaneous correlation 201 227 Instantaneous standard deviation 227 Integrability 16 18 Integral with respect to Ito process 145 Intensity of Poisson process 463 Interarrival times 463 Interest rate cap 438 Interest rate caplet 438 Interest rate models 272 Interest rate models, affine yield 274 405 Interest rate models, affine yield, canonical 405 Interest rate models, affine yield, two-factor mixed 422 Interest rate models, Brace — Gatarek — Musiela 405 see Interest rate models, Cox — Ingersoll — Ross 151 266 275 Interest rate models, Cox — Ingersoll — Ross, solution of 285 Interest rate models, Cox — Ingersoll — Ross, two-factor 420 Interest rate models, forward LIBOR 405 Interest rate models, forward LIBOR, calibration of 442 Interest rate models, Heath — Jarrow — Morton model 404 Interest rate models, Heath — Jarrow — Morton model, calibration of 432 Interest rate models, Heath — Jarrow — Morton model, multi-factor 458 Interest rate models, Heath — Jarrow — Morton model, no-arbitrage condition 428 Interest rate models, Heath — Jarrow — Morton model, under risk-neutral measure 429 Interest rate models, Hull — White 265 274 Interest rate models, Hull — White, solution of 285 Interest rate models, market 405 Interest rate models, one-factor 272 Interest rate models, Vasicek 151 405 431 Interest rate models, Vasicek, forward measure in 457 Interest rate models, Vasicek, statistics for 451 Interest rate models, Vasicek, two-factor 406 Interest rate swap 459 Intrinsic value 339 Iterated conditioning 70 Ito integral of deterministic integrand 149 173 Ito integral of general process 134 Ito integral of Ito process 145 Ito integral of simple process 127 Ito process 143 Ito process, integral with respect to 145 Ito process, quadratic variation 143 Ito — Doeblin formula, for Brownian motion 138 Ito — Doeblin formula, for Ito process 143 146 Ito — Doeblin formula, for jump processes 484 489 Ito — Doeblin formula, in differential form 137 Ito — Doeblin formula, in integral form 137 Ito — Doeblin formula, two-dimensional 167 Ito’s product rule 168 489 Jensen’s Inequality 18 Jensen’s inequality, conditional 70 Joint density 57 Joint distribution 57 Jump process 475 Jump process, continuous part 475 Jump process, cross variation 480 Jump process, Ito integral part 474 Jump process, Ito — Doeblin formula 484 489 Jump process, Ito’s product rule 489 Jump process, pure jump part 475 Jump process, quadratic variation 479 Jump process, Riemann integral part 474 Jump process, stochastic integral with respect to 475 Knock-in options 299 Knock-out options 299 Kolmogorov backward equation 291 Kolmogorov forward equation 291 Kronecker delta 201 kurtosis 117 Lebesgue integral 15 Lebesgue integral, comparison property for 16 18 Lebesgue integral, comparison with Riemann integral 22 Lebesgue integral, linearity 16 18 Lebesgue measure 3 20 Levy’s theorem, one-dimensional 168 Levy’s theorem, two-dimensional 170 LIBOR (London interbank offered rate) 405 LIBOR (London interbank offered rate), backset 437 LIBOR (London interbank offered rate), tenor of 437 Linear complementarity 352 357 Local martingale 188 Local time 205 Local time, of Brownian motion 207 Log-normal distribution 92
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