Stochastic Calculus for Finance I: The Binomial Asset Pricing Model

Steven E. Shreve

Springer, Jun 28, 2005 - Business & Economics - 187 pages

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.

What people are saying

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

User Review  - Joecolelife - Goodreads

I am always a fan of books that can simplify advanced concepts instead of drowning the reader in rigour. Shreve's introduction to probablistic asset pricing is gentle, covering basic stochastic ...

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 ...

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
• 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
• 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
• 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

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.‎

About the author

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.

Bibliographic information

• Title: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model; Volume 45 of Applications of mathematics; Springer Finance, ISSN 1616-0533; Springer finance: Textbook; Volume 1 of Stochastic Calculus for Finance, Steven E. Shreve, ISBN 0387401008, 9780387401003; Stochastic calculus for finance 1: the binomial asset pricing model, Steven E. Shreve
• Author: Steven E. Shreve
• Edition: illustrated
• Publisher: Springer, 2005
• ISBN: 0387249680, 9780387249681
• Length: 187 pages
• Subjects: Business & Economics / Finance; Mathematics / Applied; Mathematics / Game Theory; Mathematics / Probability & Statistics / General