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Shreve S.E. — Stochastic Calculus for Finance 1
Shreve S.E. — Stochastic Calculus for Finance 1

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Название: Stochastic Calculus for Finance 1

Автор: Shreve S.E.

Аннотация:

This book evolved from the first ten years of the Carnegie Mellon professional Master’s program in Computational Finance. The contents of the book have 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 refined through classroom experience with this material, are provided throughout the book. Volume I introduces the fundamental concepts in a discrete-time setting and Volume II builds on this foundation to develop stochastic calculus, martingales, risk-neutral pricing, exotic options, and term structure models, all in continuous time. 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. Classroom-tested exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance. Instructor's manual available.


Язык: en

Рубрика: Экономика и финансы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 250

Добавлена в каталог: 28.06.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Actual probability measure      61 80
Adapted      36
Adapted stochastic process      36
American call option      111 115
American derivative security      90 101 113
American put option      91
American put option, estimating price      116
Arbitrage      2 18
Arbitrage pricing theory      1 3 18
Asian option      22 59—60
Bellman equation      136 137
Bermudan option      89
Bid-ask spread      5
Binomial asset pricing model multiperiod      12
Binomial asset pricing model no arbitrage in      41
Binomial asset pricing model one-period      1
Black caplet formula      174
Bond coupon-paying      153
Bond zero-coupon      143 145
Call option American      111 115
Call option European      3 58
CAP      157
Capital asset pricing model      70
Caplet      158
Cash flow valuation      42
Chooser option      59
Complete model      14
Concave function      71
Concave function strictly      71
Conditional expectation      32 53 150
Conditional expectation independence      33
Conditional expectation iterated conditioning      33
Conditional expectation linearity      33
Conditional expectation taking out what is known      33
Conditional probability      150
Coupon-paying bond      153
Delivery date      154
Delivery price      154
Delta-hedging formula      6
Derivative security American      90 101 113
Derivative security American price (value) of      101 114
Derivative security European      5 18 42 53
Discount process      145
Discounted American derivative security price      104
Discounted American derivative security price, supermartingale under risk-neutral measure      104 114
Discounted derivative security price      42
Discounted derivative security price martingale under risk-neutral measure      42
Discounted stock price      36
Discounted stock price martingale under risk-neutral measure      53 58
Discounted wealth process      40 151
Discounted wealth process martingale under risk-neutral measure      40 151
Discounted zero-coupon bond price      150
Discounted zero-coupon bond price martingale under risk-neutral measure      151
Discrete-time stochastic integral      56
Distribution of a random variable      27
Dividend-paying stock      58
Down factor      2
Early exercise premium      89
Equivalent probability measures      84
European call      3
European call option      3 58
European derivative security      5 18 42 53
European put      5
European put option      5 58
Event      26
Expectation (expected value)      29 52
Feynman — Kac theorem      52
Finite probability space      26
First Fundamental Theorem of Asset Pricing      41
First passage time for random walk distribution      126 127 137 139
First passage time for random walk expectation      124 137 139
First passage time for random walk finiteness      122 136 139
First passage time for random walk moment generating function      137 139
First passage time for random walk moment-generating function      123
Fixed income assets      143
FLOOR      158
Floorlet      158
Forward contract      5 59 154
Forward interest rate      155
Forward LIBOR models      174
Forward measure      161
Forward price      59 154
Forward price martingale under forward measure      162
Futures contract      168
Futures price      168
HARA (Hyperbolic absolute risk aversion) utility function      71
Hedging long position      21 22
Hedging short position      5 18 114 140
Hedging static      59 154
Independence      33
Independence lemma      46
Index of absolute risk aversion      71
Interest rate      2
Interest rate cap      157
Interest rate caplet      158
Interest rate floor      158
Interest rate floorlet      158
Interest rate forward      155
Interest rate random      22 85 144
Interest rate swap      156
Intrinsic value      89 91 113
Iterated conditioning      33
Jensen's inequality      30
Jensen's inequality conditional      34
Lookback      14
Lookback option      14
Market models      174
Marking to market      169
Markov process      45 54
Markov process multidimensional      49
Martingale      36 53
Martingale transform      56
Martingale under risk-neutral measure      38
Maximum-to-date for random walk      140
Maximum-to-date for random walk joint distribution with random walk      140
Net present value      43
No-arbitrage in binomial model      152
No-arbitrage in binomialmodel      41
No-arbitrage price      4 12 18
Optimal exercise time      90 109 114
Optimal investment      72 82
Option American call      111 115
Option American put      91
Option American put estimating price      116
Option American straddle      115
Option Asian      22 59
Option Bermudan      89
Option chooser      59
Option European call      58
Option European put      58
Option perpetual American call      141
Option perpetual American put      129
Option perpetual American put short position hedge      140
Optional sampling      99 100 115
Path-dependent option      14
Perpertual American call      111 115
Perpetual American put      129
Perpetual American put short position hedge      140
Portfolio (wealth) process      40 53
Probability measure      26 52
Put option American      91 129
Put option American estimating price      116
Put option European      5 58
Radon — Nikodym derivative      61
Radon — Nikodym derivative process      67 81
Random interest rate      57
Random variable      27 52
Random variable degenerate      27
Random walk (see also first passage time, maximum to-date) asymmetric      120
Random walk (see also first passage time, maximum to-date) symmetric      120
Reflection principle      127 137
Replicating portfolio, replication multiple periods      12
Replicating portfolio, replication one period      4—5
Replicating portfolio, replication static      59 154
Risk-neutral American pricing formula      101
Risk-neutral pricing formula      7 11 42 53 54 56—59
Risk-neutral probabilities      7 19
Sample space      26 52
Short position      107
Short-rate models      144
State price      64 82
State price density      64 81
State price density process      70
State variable      48
Static hedge      59 154
Stochastic process      11
Stochastic process adapted      36
Stochastic volatility      22 57 85
Stopped process      97
Stopping time      97 114
Straddle      115
Strike price      3
Submartingale      36
Supermartingale      37
Swap rate      156
symmetric      55
Taking out what is known      33
Term structure of interest rates      143
Up factor      2
Utility function      71
Variance      29
Volatility      22 57 85
Wealth (portfolio) process      53
Wealth equation      11 39
Wealth process      40
Whole yield models      144
Zero-coupon bond      143 145
Zero-coupon bond face maturity      143
Zero-coupon bond face value      143
Zero-coupon bond par value      143
Zero-coupon bond price      150
Zero-coupon bond yield      143 145
Zero-coupon bond yield curve      143
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