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Estimation and Inference with the Efficient Method of Moments: With
Applications to Stochastic Volatility Models and Option Pricing
van der Sluis, P.J.
Publication date
1999
Link to publication
Citation for published version (APA):
van der Sluis, P. J. (1999). Estimation and Inference with the Efficient Method of Moments:
With Applications to Stochastic Volatility Models and Option Pricing. Thela Thesis. TI
Research Series nr. 204.
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Contents
1 Introduction 1
1.1 Motivation 1 1.2 Outline 2
2 Analysis of Financial Time Series 7
2.1 Characteristics of Financial Time Series 7
2.1.1 Nature of the Data 8 2.1.2 Risk versus Return 8 2.1.3 Empirical Regularities 10
2.2 Models for Volatility 13 2.2.1 Observation-driven Models 15
2.2.2 Parameter-driven Models 17 2.3 Estimation Methods for SV Models 24
2.3.1 Likelihood-based Techniques 26 2.3.2 Moment-based Techniques 29
2.4 Option Pricing 33 2.4.1 Option Pricing in Discrete Time 35
2.4.2 Testing Option Pricing Models 36
3 Efficient Method of Moments 39
3.1 Theory 39 3.1.1 Estimation 40
3.1.2 Inference 46 3.2 EMM for SV Models 50
3.2.1 Score Generators 50 3.2.2 Continuous-time versus Discrete-time SV Models 52
3.2.3 Reprojection 52 3.3 Implementation of EMM 56 3.4 Monte Carlo Results 57 3.5 Application to Daily Returns of S&P500 1963-1993 66
viii CONTENTS
4 Stability Tests with Known Breakpoint 71
4.1 Introduction 71 4.2 First-order EMM Estimators 73
4.3 Stability Tests with Known Breakpoint for EMM 76
4.3.1 Prediction Tests 78 4.3.2 Wald-type Tests 79 4.3.3 Hansen-type Tests 81 4.3.4 Issues Specific to EMM-based Tests 82
4.4 Application to SV Models 84 4.4.1 Monte Carlo Results 84 4.4.2 Application to Exchange Rates 93
4.4.3 Application to Daily Returns of S&P500 1981-1993 . . . 98
4.5 Conclusion 101 4.A Appendix: Proof of Theorem 4.1 103
5 Stability Tests with Unknown Breakpoint 105
5.1 Introduction 105 5.2 Stability Tests with Unknown Breakpoint for EMM 107
5.2.1 Wald-type Tests 107 5.2.2 Prediction Tests 109 5.2.3 Hansen-type Tests I l l 5.2.4 Hall-Sen-type Tests I l l 5.2.5 Practical Issues of the Tests and Critical Values 112
5.3 Application to SV Models 113 5.3.1 Description of the Data and the Model 113
5.3.2 Implementation, Estimation and Tests 114
5.3.3 Discussion of Results 115
5.4 Conclusion 121 5.A Appendix: Proof of Theorem 5.1 122
6 Option Pricing 127
6.1 Introduction 127 6.2 Model 130 6.3 Estimation 131
6.3.1 Estimation Technique 131 6.3.2 Description of the Data 133 6.3.3 Structural Models and Estimation Results 138
6.4 Pricing of Stock Options 143 6.4.1 Description of the Option Data 144
6.4.2 Testing Option Pricing Models 146 6.4.3 Comparison based on Diversifiable Stochastic Volatility Risk 149
CONTENTS ix
6.4.4 Comparison based on Implied Stochastic Volatility Risk .154
6.5 Conclusion 158
7 Forecasting Volatility 161
7.1 Introduction 161 7.2 Data, Models and Estimation 162
7.2.1 Data and Notation 162
7.2.2 Models 163 7.3 Forecasting Volatility based on SV Models 166
7.3.1 Volatility Forecasting based on Univariate SV Models . . 170 7.3.2 Volatility Forecasting based on Multivariate SV Models . . 174
7.4 Conclusion 176
8 Summary and Further Research 177
8.1 Summary 177 8.2 Outlook for Further Research 180
A Description of Code and Score Generators 183
A. 1 Description of EmmPack and Ox 184 A.2 Description of the Auxiliary Model 188 A.3 Derivatives of EGARCH Process 191 A.4 Derivatives of EGARCH-t Process 192 A.5 Derivatives of MEGARCH Process 193
A.6 Antithetic Variables 195
Nederlandse Samenvatting (Summary in Dutch) 197
Bibliography 203 Author Index 221
