## Forecasting and Hedging in the Foreign Exchange MarketsHistorical and recent developments at international ?nancial markets show that it is easy to loose money, while it is dif?cult to predict future developments and op- mize decision-making towards maximizing returns and minimizing risk. One of the reasons of our inability to make reliable predictions and to make optimal decisions is the growing complexity of the global economy. This is especially true for the f- eign exchange market (FX market) which is considered as one of the largest and most liquid ?nancial markets. Its grade of ef?ciencyand its complexityis one of the starting points of this volume. From the high complexity of the FX market, Christian Ullrich deduces the - cessity to use tools from machine learning and arti?cial intelligence, e.g., support vector machines, and to combine such methods with sophisticated ?nancial mod- ing techniques. The suitability of this combination of ideas is demonstrated by an empirical study and by simulation. I am pleased to introduce this book to its - dience, hoping that it will provide the reader with interesting ideas to support the understanding of FX markets and to help to improve risk management in dif?cult times. Moreover, I hope that its publication will stimulate further research to contribute to the solution of the many open questions in this area. |

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### Contents

2 | |

3 | |

7 | |

8 | |

10 | |

Foreign Exchange Market Predictability | 13 |

Equilibrium Relationships | 14 |

312 Relative PPP | 16 |

104 Kernel Selection | 91 |

105 Cross Validation | 94 |

106 Benchmark Models | 95 |

107 Evaluation Procedure | 97 |

1072 Operational Evaluation | 98 |

108 Numerical Results and Discussion | 99 |

Exchange Rate Hedging in a SimulationOptimization Framework | 104 |

Introduction | 105 |

313 Empirical Evidence | 17 |

314 Explanations for Deviations from PPP | 19 |

32 Interest Rate Parity IRP Theorem | 21 |

322 Uncovered Covered Interest Rate Parity UIP | 22 |

324 Explanations for Deviations from IRP | 24 |

Market Efﬁciency Concepts | 27 |

42 Speculative Efﬁciency | 28 |

Views from Complexity Theory | 29 |

52 Calculating Fixed Point Market Equilibrium | 32 |

522 Computational Complexity of Decentralized Equilibrium | 33 |

523 AdaptiveInductive Learning of Rational Expectations Equilibria | 34 |

53 Computational Difﬁculties with Efﬁciency | 35 |

532 Computational Complexity of Arbitrage | 37 |

Conclusions | 38 |

Exchange Rate Forecasting with Support Vector Machines | 39 |

Introduction | 40 |

Statistical Analysis of Daily Exchange Rate Data | 47 |

821 Stationarity | 50 |

822 Normal Distribution | 53 |

823 Linearity | 54 |

824 Heteroskedasticity | 57 |

825 Nonlinearity | 61 |

826 Results | 63 |

Support Vector Classiﬁcation | 64 |

93 Supervised Learning | 67 |

94 Structural Risk Minimization | 69 |

95 Support Vector Machines | 71 |

952 Kernel Functions | 72 |

953 Optimal Separating Hyperplane | 73 |

954 Generalized Optimal Separating Hyperplane | 79 |

955 Generalization in High Dimensional Feature Space | 81 |

Description of Empirical Study and Results | 83 |

Input Data Selection | 84 |

102 SVM Model | 89 |

Preferences over Probability Distributions | 117 |

1212 Plain Vanilla Option | 119 |

1213 Straddle | 121 |

122 Formal Relationship Between Firm and Capital Market Expectations | 122 |

123 Speciﬁcation of Probability Distribution Function | 123 |

124 Expected Utility Maximization and ThreeMoments Ranking | 124 |

1242 Preference Structures over Utility Functions | 126 |

1244 Increasing Wealth Preference | 127 |

1246 Ruin Aversion Preference | 128 |

125 Speciﬁcation of Utility Function | 129 |

Problem Statement and Computational Complexity | 132 |

132 Computational Complexity Considerations | 135 |

1322 Complexity of Stochastic Combinatorial Optimization | 137 |

1323 Objective Function Characteristics | 139 |

Model Implementation | 141 |

142 Simulation Model | 142 |

Equilibrium | 143 |

Nonlinear Mean Reversion | 145 |

Gaussian Random Walk | 148 |

1425 Aggregation of Components | 150 |

1426 Calibration of Parameters | 151 |

143 Optimization Model | 152 |

1432 Scatter Search and Path Relinking | 154 |

SimulationOptimization Experiments | 163 |

1522 Data Inputs and Parameters | 164 |

1523 Evaluation Procedure | 170 |

153 Results | 173 |

1532 Ex Post Performance | 176 |

Contributions of the Dissertation | 180 |

Exchange Rate Forecasting with Support Vector Machines | 183 |

Exchange Rate Hedging in a SimulationOptimization Framework | 185 |

References | 190 |

References | 191 |

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### Common terms and phrases

algorithm arbitrage autoregressive backtesting behavior Berlin Heidelberg 2009 classiﬁcation combinatorial optimization component computational complexity currency pair dataset deﬁned Deﬁnition denote deterministic deviations difﬁcult diversiﬁcation dynamic Econ empirical equilibrium estimated EUR/GBP EUR/JPY EUR/USD exchange rate returns exposure feature space ﬁnancial market ﬁnd ﬁnding ﬁrm ﬁrm’s ﬁrst ﬁxed point Forecasting and Hedging Foreign Exchange Markets forward contract GARCH given Granger cause hedge intensity hyperplane hypothesis space input interest rate investors kernel learning linear margin market efﬁciency Mathematical Systems 623 maximization mean-variance-skewness metaheuristic methods nonlinear NP-complete null hypothesis optimization problem p-Gaussian parameters Parity payoff polynomial positive predict probability distribution procedure proﬁt random real exchange rate RefSet risk aversion risk management scatter search signiﬁcant simulation Simulation/Optimization skewness solutions solved speciﬁc spot exchange rate stochastic straddle strategy subset supervised learning Support Vector Machines theory tion trading Ullrich utility function variance volatility