Financial Risk Management with Bayesian Estimation of GARCH Models

1. Front Matter

   Pages I-XIII

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2. Introduction

   Pages 1-7

3. Bayesian Statistics and MCMC Methods

   Pages 9-15

4. Bayesian Estimation of the GARCH(1, 1) Model with Normal Innovations

   Pages 17-37

5. Bayesian Estimation of the Linear Regression Model with Normal-GJR(1, 1) Errors

   Pages 39-54

6. Bayesian Estimation of the Linear Regression Model with Student-t-GJR(1, 1) Errors

   Pages 55-71

7. Value at Risk and Decision Theory

   Pages 73-107

8. Bayesian Estimation of the Markov-Switching GJR(1, 1) Model with Student-t Innovations

   Pages 109-153

9. Conclusion

   Pages 155-159

10. Back Matter

    Pages 161-203

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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.

• Bayesian
• Financial Risk Management
• GARCH
• MCMC
• Risk Management
• decision theory
• regression
• statistics
• value at risk
• value-at-risk
• quantitative finance

From the reviews: “This book provides an application of Bayesian methods to financial risk management. … The book is well written, it provides a comprehensive list of references and its index allows very easy navigation among its different concepts. This book can be very useful to graduate students as well as researchers who work on quantitative risk management and/or financial econometrics. … To sum up, the book is well organized and provides a thorough treatment of the Bayesian estimation of GARCH-like models and its application to risk management.” (Yannick Malevergne, Mathematical Reviews, Issue 2010 b)

• University of Fribourg, 1700, Switzerland

  David Ardia

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