Stochastic Calculus for Finance I / Edition 1

by Steven E. Shreve

Overview

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S.

Has been tested in the classroom and revised over a period of several years

Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

Product Details

ISBN-13:	9780387401003
Publisher:	Springer New York
Publication date:	03/01/2004
Series:	Springer Finance / Springer Finance Textbooks Series
Edition description:	2004
Pages:	187
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. The Binomial No-Arbitrage Pricing Model
1.1. One-Period Binomial Model
1.2. Multiperiod Binomial Model
1.3. Computational Considerations
1.4. Summary
1.5. Notes
1.6. Exercises 2. Probability Theory on Coin Toss Space
2.1. Finite Probability Spaces
2.2. Random Variables, Distributions, and Expectations
2.3. Conditional Expectations
2.4. Martingales
2.5. Markov Processes
2.6. Summary
2.7. Notes
2.8. Exercises 3. State Prices
3.1. Change of Measure
3.2. Radon-Nikod\'ym Derivative Process
3.3. Capital Asset Pricing Model
3.4. Summary
3.5. Notes
3.6. Exercises 4. American Derivative Securities
4.1. Introduction
4.2. Non-Path-Dependent American Derivatives
4.3. Stopping Times
4.4. General American Derivatives
4.5. American Call Options
4.6. Summary
4.7. Notes
4.8. Exercises 5. Random Walk
5.1. Introduction
5.2. First Passage Times
5.3. Reflection Principle
5.4. Perpetual American Put: An Example
5.5. Summary
5.6. Notes
5.7. Exercises 6. Interest-Rate-Dependent Assets
6.1. Introduction
6.2. Binomial Model for Interest Rates
6.3. Fixed-Income Derivatives
6.4. Forward Measures
6.5. Futures
6.6. Summary
6.7. Notes
6.8. Exercises Proof of Fundamental Properties of Conditional Expectations
References
Index