Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Google eBook)

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Springer Science & Business Media, Jun 28, 2005 - Business & Economics - 187 pages
5 Reviews
This book evolved from the first ten years of the Carnegie Mellon professional Masterbs 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.

  

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Review: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model

User Review  - Joecolelife - Goodreads

Shreve's book is an excellent introduction to basic options pricing. He not only deals with plain vanilla options, but also shows how the binomial model can be used to to value exotic options. Each ... Read full review

Contents

The Binomial NoArbitrage Pricing Model
1
12 Multiperiod Binomial Model
8
13 Computational Considerations
15
14 Summary
18
15 Notes
20
Probability Theory on Coin Toss Space
25
22 Random Variables Distributions and Expectations
27
23 Conditional Expectations
31
45 American Call Options
111
46 Summary
113
47 Notes
115
Random Walk
119
52 First Passage Times
120
53 Reflection Principle
127
An Example
129
55 Summary
136

24 Martingales
36
25 Markov Processes
44
26 Summary
52
27 Notes
54
State Prices
61
32 RadonNikodym Derivative Process
65
33 Capital Asset Pricing Model
70
34 Summary
80
35 Notes
83
American Derivative Securities
89
42 NonPathDependent American Derivatives
90
43 Stopping Times
96
44 General American Derivatives
101
56 Notes
138
InterestRateDependent Assets
143
62 Binomial Model for Interest Rates
144
63 FixedIncome Derivatives
154
64 Forward Measures
160
65 Futures
168
66 Summary
173
67 Notes
174
Proof of Fundamental Properties of Conditional Expectations
177
References
181
Index
185
Copyright

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Popular passages

Page 182 - Department of Mathematical Sciences, Carnegie Mellon University. 20. HEATH. D., JARROW, R., & MORTON, A. (1gg2) Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica 60, 77-105. 21. HEATH, D., JARROW, R., & MORTON, A.
Page 181 - TOY, W. (1gg0) A one-factor model of interest rates and its application to treasury bond options, Fin.

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About the author (2005)

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.