Financial Risk Management with Bayesian Estimation of GARCH Models (eBook)

Preface 7
Table of Contents 9
Summary 12
1 Introduction 13
Organization of the book 17
2 Bayesian Statistics and MCMC Methods 21
2.1 Bayesian inference 21
2.2 MCMC methods 22
3 Bayesian Estimation of the GARCH(1 1) Model with Normal Innovations
3.1 The model and the priors 29
3.2 Simulating the joint posterior 30
3.3 Empirical analysis 34
3.4 Illustrative applications 46
4 Bayesian Estimation of the Linear Regression Model with Normal-GJR(1 1) Errors
4.1 The model and the priors 52
4.2 Simulating the join t posterior 53
4.3 Empirical analysis 56
4.4 Illustrative applications 65
5 Bayesian Estimation of the Linear Regression Model with Student-t-GJR(1 1) Errors
5.1 The model and the priors 68
5.2 Simulating the joint posterior 71
5.3 Empirical analysis 76
5.4 Illustrative applications 83
6 Value at Risk and Decision Theory 85
6.1 Introduction 85
6.2 The concept of Value at Risk 88
6.3 Decision theory 97
6.4 Empirical application: the VaR term struct 103
6.5 The Expected Shortfall risk measure 116
7 Bayesian Estimation of the Markov-Switchin GJR(1 1) Model with Student-t Innovations
7.1 The model and the priors 123
7.2 Simulating the joint posterior 127
7.3 An application to the Swiss Market Index 134
7.4 In-sample performance analysis 145
7.5 Forecasting performance analysis 156
7.6 One-day ahead VaR density 160
7.7 Maximum Likelihood estimation 164
8 Conclusion 167
Suggestions for further work 170
A Recursive Transformations 173
A.1 The GARCH(1 1) model with Normal innovations
A.2 The GJR(1 1) model with Normal innovations
A.3 The GJR(1 1) model with Student-t innovations
B Equivalent Specification 177
C Conditional Moments 183
Computational Details 191
Abbreviations and Notations 193
List of Tables 199
List of Figures 201
References 203
Index 213