1 Financial Volatility Models 1
1.1 Stylized Facts 1
1.1.1 ARCH-type Model 2
1.1.2 Stochastic Volatility(SV)Model 5
1.1.3 Jump Process 7
1.2 The Relationships of the Three Models 9
1.2.1 ARCH-type and SV Models 10
1.2.2 ARCH-type and SV Models with Jump Components 11
1.2.3 Purpose for Testing 11
1.2.4 Purpose of This Book 12
1.3 Methodology 14
1.3.1 Lagrange Multiplier Test 14
1.3.2 Dirac's Delta Function 15
1.4 Structure of This Book 15
References 16
2 Testing for EGARCH against Stochastic Volatility Models 25
2.1 Introduction 25
2.2 Model and Test Statistic 26
2 3 Conclusions 40
Appendix 40
References 44
3 Testing for GARCH against Jump-GARCH Models 46
3.1 Introduction 46
3.2 Model and the Lagrange Multiplier Test Statistic 48
3.3 Simulation 56
3.4 Conclusions 59
Appendix A 60
Appendix B 65
Appendix C 68
References 73
4 Testing for Jumps in the GARCH(t)Jump Processes 75
4.1 Introduction 75
4.2 Model and Lagrange Multiplier Test Statistic 77
4.3 A Monte Carlo Experiment and an Empirical Example 85
4.4 Algebraic Details 87
References 90
5 Testing for Jumps in the EGARCH Process 93
5.1 Introduction 93
5.2 Lagrange Multiplier Test for Jump-EGARCH with Gaussian Innovations 95
5.3 Jump-EGARCH with Student-t Innovations 101
5.4 One-sided Test 104
5.5 A Monte Carlo Experiment and an Empirical Example 105
References 111
6 Tests for Jumps in Stochastic Volatility Processes 114
6.1 Introduction 114
6.2 Testing for Simple SV against SV with Jumps in Returns 116
6.2.1 SV Molde with Jumps in Returns 116
6.2.2 Test Statistic 117
6.3 Testing for Jumps in the Volatility Correlated with Jumps in Returns 120
6.3.1 Model 121
6.3.2 Test Statistic 122
6.4 Testing for Jumps in Volatility Independent of Jumps in Returns 125
6.4.1 The Model 126
6.4.2 Test Statistic 127
6.5 Empirical Examples and Monte Carlo Experiment 128
Appendix 128
References 130
后记 132