This book evolved from the first ten years of the Carnegie Mellon professional Master's 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 author does not assume familiarity with advanced mathematical concepts from measure-theoretic probability, but rather develops the necessary tools from this subject informally within the text. Many classroom-tested examples, exercises, and intuitive arguments are presented throughout the book.
Autorentext
Klappentext
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
Inhalt
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