Stochastic Calculus for Finance I / Edition 1

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This is the first volume in a two volume sequence providing the foundational material on Stochastic calculus models in finance. This first volume is suitable for discrete-time finance. The only pre-requisite is standard calculus; may aspects such as martingales and change of measure are treated in detailed depth. Probability is covered in detail using the binomial model. The book will be suitable for advanced undergraduate courses and beginning masters-level students in mathematical finance and financial engineering. There are exercises and examples throughout and summaries at the end of each chapter.

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Product Details

  • ISBN-13: 9780387401003
  • Publisher: Springer New York
  • Publication date: 3/1/2004
  • Series: Springer Finance / Springer Finance Textbooks Series
  • Edition description: 2004
  • Edition number: 1
  • Pages: 187
  • Sales rank: 417,190
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.50 (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
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