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Shreve S.E. — Stochastic Calculus for Finance 2
Shreve S.E. — Stochastic Calculus for Finance 2

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Название: Stochastic Calculus for Finance 2

Автор: 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: en

Рубрика: Экономика и финансы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 550

Добавлена в каталог: 28.06.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\sigma$-algebra ($\sigma$-field)      1
$\sigma$-algebra ($\sigma$-field), $\sigma$(X)      52
$\sigma$-algebra ($\sigma$-field), Borel      4 8 20
$\sigma$-algebra ($\sigma$-field), generated by a collection of sets      531
$\sigma$-algebra ($\sigma$-field), generated by a random variable      52
$\sigma$-algebra ($\sigma$-field), trivial      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, $\sigma$-algebra      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 $\sigma$-algebras      56
Independence among sequence of random variables      56
Independence between $\sigma$-algebras      54
Independence between normal random variables      61
Independence between random variable and $\sigma$-algebra      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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