Overview
Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives.
This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature.
This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments.
Product Details
| ISBN-13: | 9789814725910 |
|---|---|
| Publisher: | World Scientific Publishing Company, Incorporated |
| Publication date: | 01/13/2016 |
| Series: | Modern Trends In Financial Engineering , #1 |
| Pages: | 220 |
| Product dimensions: | 6.20(w) x 9.20(h) x 0.70(d) |
Table of Contents
Preface v
1 Introduction 1
1.1 Chapter Outline 3
1.2 Related Studies 7
2 Trading Under the Ornstein-Uhlenbeck Model 11
2.1 A Pairs Trading Example 11
2.2 Optimal Timing of Trades 16
2.3 Methodology 18
2.4 Analytical Results 22
2.4.1 Optimal Exit Timing 22
2.4.2 Optimal Entry Timing 25
2.5 Incorporating Stop-Loss Exit 30
2.5.1 Optimal Exit Timing 31
2.5.2 Optimal Entry Timing 34
2.5.3 Relative Stop-Loss Exit 39
2.5.4 Optimal Switching with Stop-Loss Exit 39
2.6 Further Applications 41
2.6.1 Minimum Holding Period 42
2.6.2 Path-Dependent Risk Penalty 44
2.7 Proofs of Lemmas 45
3 Trading Under the Exponential OU Model 51
3.1 Optimal Trading Problems 51
3.1.1 Optimal Double Stopping Approach 52
3.1.2 Optimal Switching Approach 53
3.2 Summary of Analytical Results 53
3.2.1 Optimal Double Stopping Problem 54
3.2.2 Optimal Switching Problem 55
3.2.3 Numerical Examples 58
3.3 Methods of Solution 61
3.3.1 Optimal Double Stopping Problem 61
3.3.2 Optimal Switching Problem 66
3.4 Proofs of Lemmas 75
4 Trading Under the CIR Model 81
4.1 Optimal Trading Problems 82
4.1.1 Optimal Starting-Stopping Approach 82
4.1.2 Optimal Switching Approach 83
4.2 Summary of Analytical Results 84
4.2.1 Optimal Starting-Stopping Problem 85
4.2.2 Optimal Switching Problem 86
4.2.3 Numerical Examples 88
4.3 Methods of Solution and Proofs 91
4.3.1 Optimal Starting-Stopping Problem 91
1.3.1 Optimal Switching Problem 99
4.4 Proofs of Lemmas 100
5 Futures Trading Under Mean Reversion 105
5.1 Futures Prices Under Mean-Reverting Spot Models 105
5.1.1 OU and CIR Spot Models 105
5.1.2 Exponential OU Spot Model 108
5.2 Roll Yield 110
5.2.1 OU and CTR Spot Models 111
5.2.2 Exponential Oil Dynamics 112
5.3 Futures Trading Problem 114
5.4 Variational Inequalities and Optimal Trading Strategies 116
5.5 Dynamic Futures Portfolios 118
5.5.1 Portfolio Dynamics with a CIR Spot 121
5.5.2 Portfolio Dynamics with an XOU Spot 123
5.6 Application to VIX Futures & Exchange-Traded Notes 125
6 Optimal Liquidation of Options 129
6.1 Optimal Liquidation with Risk Penalty 130
6.1.1 Optimal Liquidation Premium 131
6.2 Applications to GBM and Exponential OU Models 137
6.2.1 Optimal Liquidation with a GBM Underlying 137
6.2.2 Optimal Liquidation with an Exponential OU Underlying 144
6.3 Quadratic Penalty 150
6.3.1 Optimal Timing to Sell a Stock 151
6.3.2 Liquidation of Options 153
6.4 Concluding Remarks 155
6.5 Strong Solution to the Inhomogeneous Variational Inequality 157
6.5.1 Preliminaries 158
6.5.2 Main Results 160
7 Trading Credit Derivatives 163
7.1 Problem Formulation 164
7.1.1 Price Discrepancy 165
7.1.2 Delayed Liquidation Premium 166
7.2 Optimal Liquidation under Markovian Credit Risk Models 168
7.2.1 Pricing Measures and Default Risk Premia 168
7.2.2 Delayed Liquidation Premium and Optimal Timing 172
7.3 Application to Single-Name Credit Derivatives 174
7.3.1 Detail]table Bonds with Zero Recovery 175
7.3.2 Recovery of Treasury and Market Value 179
7.3.3 Optimal Liquidation of CDS 180
7.3.4 Jump-Diffusion Default Intensity 184
7.4 Optimal Liquidation of Credit Default Index Swaps 186
7.5 Optimal Buying and Selling 194
7.5.1 Optimal Timing with Short Sale Possibility 194
7.5.2 Sequential Buying and Selling 195
7.6 Concluding Remarks 197
Bibliography 201
Index 209