1 The Binomial No-Arbitrage Pricing Model 1
1.1 One-Period Binomial Model 1
1.2 Multiperiod Binomial Model 8
1.3 Computational Considerations 15
1.4 Summary 18
1.5 Notes 20
1.6 Exercises 20
2 Probability Theory on Coin Toss Space 25
2.1 Finite Probability Spaces 25
2.2 Random Variables， Distributions， and Expectations 27
2.3 Conditional Expectations 31
2.4 Martingales 36
2.5 Markov Processes 44
2.6 Summary 52
2.7 Notes 54
2.8 Exercises 54
3 State Prices 61
3.1 Change of Measure 61
3.2 Radon-Nikodym Derivative Process 65
3.3 Capital Asset Pricing Model 70
3.4 Summary 80
3.5 Notes 83
3.6 Exercises 83
4 American Derivative Securities 89
4.1 Introduction 89
4.2 Non-Path-Dependent American Derivatives 90
4.3 Stopping Times 96
4.4 General American Derivatives 101
4.5 American Call Options 111
4.6 Summary 113
4.7 Notes 115
4.8 Exercises 115
5 Random Walk 119
5.1 Introduction 119
5.2 First Passage Times 120
5.3 Reflection Principle 127
5.4 Perpetual American Put： An Example 129
5.5 Summary 136
5.6 Notes 138
5.7 Exercises 138
6 Interest-Rate-Dependent Assets 143
6.1 Introduction 143
6.2 Binomial Model for Interest Rates 144
6.3 Fixed-Income Derivatives 154
6.4 Forward Measures 16
6.5 Futures 168
6.6 Summary 173
6.7 Notes 174
6.8 Exercises 174
Proof of Fundamental Properties of Conditional Expectations 177
References 181
Index 185