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

Theory and Applications

David Ardia (Autor)

eBook Download: PDF

2008 | 2008
XIV, 206 Seiten
Springer Berlin (Verlag)
978-3-540-78657-3 (ISBN)

Infos

This book presents in detail methodologies for the Bayesian estimation of sing- regime and regime-switching GARCH models. These models are widespread and essential tools in n ancial econometrics and have, until recently, mainly been estimated using the classical Maximum Likelihood technique. As this study aims to demonstrate, the Bayesian approach o ers an attractive alternative which enables small sample results, robust estimation, model discrimination and probabilistic statements on nonlinear functions of the model parameters. The author is indebted to numerous individuals for help in the preparation of this study. Primarily, I owe a great debt to Prof. Dr. Philippe J. Deschamps who inspired me to study Bayesian econometrics, suggested the subject, guided me under his supervision and encouraged my research. I would also like to thank Prof. Dr. Martin Wallmeier and my colleagues of the Department of Quantitative Economics, in particular Michael Beer, Roberto Cerratti and Gilles Kaltenrieder, for their useful comments and discussions. I am very indebted to my friends Carlos Ord as Criado, Julien A. Straubhaar, J er ^ ome Ph. A. Taillard and Mathieu Vuilleumier, for their support in the elds of economics, mathematics and statistics. Thanks also to my friend Kevin Barnes who helped with my English in this work. Finally, I am greatly indebted to my parents and grandparents for their support and encouragement while I was struggling with the writing of this thesis.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 8.5.2008
• Reihe/Serie: Lecture Notes in Economics and Mathematical Systems
• Reihe/Serie: Lecture Notes in Economics and Mathematical Systems
• Zusatzinfo: XIV, 206 p. 27 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Bayesian • Decision Theory • financial risk management • GARCH • MCMC • Quantitative Finance • Regression • Risk Management • Statistics • Value at risk • Value-at-Risk
• ISBN-10: 3-540-78657-0 / 3540786570
• ISBN-13: 978-3-540-78657-3 / 9783540786573