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1. Introduction 1
2. Financial Markets 5
2.1 Market Price Formation 5
2.2 Returns and Dividends 7
2.2.1 Simple and Compounded Returns 7
2.2.2 Dividend Effects 8
2.3 Market Efficiency 11
2.3.1 Arbitrage 11
2.3.2 Efficient Market Hypothesis 12
2.4 Pathways for Further Reading 14
2.5 Exercises 15
3. Probability Distributions 17
3.1 Basic Definitions 17
3.2 Important Distributions 20
3.3 Stable Distributions and Scale Invariance 25
3.4 References for Further Reading 27
3.5 Exercises 27
4. Stochastic Processes 29
4.1 Markov Processes 29
4.2 Brownian Motion 32
4.3 Stochastic Differential Equation 35
4.4 Stochastic Integral 36
4.5 Martingales 39
4.6 References for Further Reading 41
4.7 Exercises 419.6 Appendix. The Invariant of the Arbitrage-Free
Portfolio 105
9.7 Exercises 109
10. Portfolio Management 111
10.1 Portfolio Selection 111
10.2 Capital Asset Pricing Model (CAPM) 114
10.3 Arbitrage Pricing Theory (APT) 116
10.4 Arbitrage Trading Strategies 118
10.5 References for Further Reading 120
10.6 Exercises 120
11. Market Risk Measurement 121
11.1 Risk Measures 121
11.2 Calculating Risk 125
11.3 References for Further Reading 127
11.4 Exercises 127
12. Agent-Based Modeling of Financial Markets 129
12.1 Introduction 129
12.2 Adaptive Equilibrium Models 130
12.3 Non-Equilibrium Price Models 134
12.4 Modeling of Observable Variables 136
12.4.1 The Framework 136
12.4.2 Price-Demand Relations 138
12.4.3 Why Technical Trading May Be Successful 139
12.4.4 The Birth of a Liquid Market 141
12.5 References for Further Reading 143
12.6 Exercises 143
Comments 145
References 149
Answers to Exercises 159
Index 161
Detailed Table of Contents ix
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