Stochastic Calculus Models for Finance The Binomial Asset Pricing Model

ISBN-10: 0387401008

ISBN-13: 9780387401003

Edition: 2004

Authors: Steven E. Shreve

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Description:

This book evolved from the first ten years of the Carnegie Mellon professional Masters 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.        
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Book details

List price: $54.95
Copyright year: 2004
Publisher: Springer
Publication date: 4/21/2004
Binding: Hardcover
Pages: 187
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.232
Language: English

The Binomial No-Arbitrage Pricing Model
One-Period Binomial Model
Multiperiod Binomial Model
Computational Considerations
Summary
Notes
Exercises
Probability Theory on Coin Toss Space
Finite Probability Spaces
Random Variables, Distributions, and Expectations
Conditional Expectations
Martingales
Markov Processes
Summary
Notes
Exercises
State Prices
Change of Measure
Radon-Nikod'ym Derivative Process
Capital Asset Pricing Model
Summary
Notes
Exercises
American Derivative Securities
Introduction
Non-Path-Dependent American Derivatives
Stopping Times
General American Derivatives
American Call Options
Summary
Notes
Exercises
Random Walk
Introduction
First Passage Times
Reflection Principle
Perpetual American Put: An Example
Summary
Notes
Exercises
Interest-Rate-Dependent Assets
Introduction
Binomial Model for Interest Rates
Fixed-Income Derivatives
Forward Measures
Futures
Summary
Notes
Exercises Proof of Fundamental Properties of Conditional Excectations
References
Index
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