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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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Long rate 273 413 Lookback option 308 335 Market model 405 Market price of risk 204 216 228 Market price of risk in Heath — Jarrow — Morton model 427 Market price of risk in jump-diffusion model 515 Marking to market 243 Markov process 74 Martingale 74 Martingale Representation Theorem, multi-dimensional 225 Martingale Representation Theorem, one-dimensional 221 Martingale, exponential 109 Martingale, local 188 Mean reversion in Vasicek model 151 Mean value theorem 44 100 Measurability of a random variable 53 Measure, distribution 9 Measure, Lebesgue 3 20 Measure, probability 2 Measure, uniform 3 Memorylessness 463 Moment-generating function 43 Moment-generating function for Brownian motion 96 Moment-generating function of standard normal random variable 45 Money market account 272 Monotone Convergence Theorem 26 No-arbitrage derivation of bond price 282 Normal random variable(s), jointly 64 Normal random variable(s), kurtosis 117 Normal random variable(s), moment generating function 45 Normal random variable(s), uncorrelated and dependent 62 Numeraire 375 Optimal exercise time 340 Option pricing with random interest rate 394 Option, American 339 Option, American, perpetual put 345 Option, Asian option 278 320 Option, Asian option, discretely sampled 329 Option, Asian option, zero-strike call 336 Option, barrier 299 Option, Bermudan option 339 Option, chooser 256 Option, European call 155 Option, European put 163 Option, exotic 295 Option, knock-in 299 Option, knock-out 299 Option, lookback 308 335 Option, on a bond 276 Option, path-dependent 295 Option, quanto 401 Option, up-and-out call 307 332 Option, vanilla 295 Optional sampling 302 342 373 Ornstein — Uhlenbeck process 286 Partial averaging 68 Path-dependent option 295 Perpetual American put 345 Poisson process 463 Poisson process, compensated 467 Poisson process, compound 468 Poisson process, expected value 467 Poisson process, geometric 486 Poisson process, intensity 463 Poisson process, moment generating function 471 Poisson process, relative to a filtration 473 Poisson process, variance 467 Portfolio value process 154 Predictable 477 Principal components analysis 434 Probability integral transform 12 Probability measure 2 Probability space 2 Probability space, coin toss 4 Pure jump process 475 Put option, European 163 Put-call parity 164 Quadratic variation 101 Quadratic variation for Brownian motion 102 Quadratic variation for Ito process 143 Quadratic variation for jump process 479 Quanto option 401 Radon — Nikodym, derivative 36 210 Radon — Nikodym, derivative process 211 Radon — Nikodym, theorem 39 Random variable 7 Random variable, degenerate 77 Random variable, exponential 462 Random variable, indicator 17 Random variable, standard normal 12 Random walk see “symmetric random walk” Reflection principle 111 Relative maturity 412 Riemann integral 14 Riemann integral, comparison with Lebesgue integral 22 Riemann integral, not defined 20 Riemann sum, lower 13 Riemann sum, upper 13 Risk-neutral measure 216 228 Risk-neutral measure, domestic 383 Risk-neutral measure, existence 231 Risk-neutral measure, foreign 386 Risk-neutral measure, implying from option prices 255 Risk-neutral measure, uniqueness 232 Risk-neutral pricing formula 218 Risk-neutral pricing formula for a cash flow 246 Sample space 1 Self-financing trading 193 397 Sets resolved by information 49 Short rate models see “Interest rate models” Siegel’s exchange rate paradox 387 Simple process 126 Singularly continuous function 310 St. Petersburg paradox 27 Standard deviation 62 Standard deviation, instantaneous 227 Standard normal 12 Standard normal, density 12 Standard normal, distribution 12 Standard normal, random variable 12 State price density 204 252 State processes 281 State processes, augmentation of 321 Static hedge 162 Stationary increments 466 Statistical arbitrage 188 Stochastic differential equation 263 Stochastic differential equation, one-dimensional linear 264 Stop-loss start-gain paradox 207 Stopped process 342 Stopping set 355 357 Stopping time 302 341 Stratonovich integral 136 190 Strong Law of Large Numbers 7 23 Submartingale 74 Supermartingale 74 Swap 459 see Swap rate 459 Symmetric random walk 84 Symmetric random walk, independent increments 84 Symmetric random walk, martingale property 85 Symmetric random walk, quadratic variation 85 Symmetric random walk, scaled 86 Tenor 437 Theta 159 193 Time spread 452 Uncorrelated dependent Brownian motions 204 Uncorrelated random variables 62 Uncorrelated random variables, dependent normal random variables 62 Uncountably infinite set 1 41 Uniform measure (distribution) 3 19 Up-and-out call price 307 332 Vanilla option 295 Variance 62 Vasicek equation 191 Vasicek interest rate model 151 405 431 Vasicek interest rate model, forward measure in 457 Vasicek interest rate model, mean reversion in 151 Vasicek interest rate model, statistics for 451 Vasicek interest rate model, two-factor 406 Vega 162 Volatility 106 Volatility, implied 271 Volatility, smile 271 Volatility, surface 293 Volatility, vector 377 Yield 273 403 Yield, affine 274 Yield, curve 404 Zero-coupon bond 240 273
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