Measuring tail thickness under GARCH and an application to extreme exchange rate changes |
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| Institution: | 1. Universitat Autònoma de Barcelona, Barcelona Graduate School of Economics, Spain;2. MOVE, Spain;3. University College London, CEMMAP (Centre for Microdata Methods and Practice, IFS), United Kingdom;4. CREATES (Center For Research in Econometric Analysis of Time Series), University of Aarhus, Denmark;1. Department of Economics and Social Sciences, Faculty of Economics “G. Fuá”, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy;2. Department of Economics, New York University, 269 Mercer Street, NY 10003, New York, USA;1. Department of Management and Department of Economics, College of Business and Economics, California State University, East Bay, Hayward, CA 94542, United States;2. Department of Accounting and Finance, College of Business and Economics, California State University, East Bay, Hayward, CA 94542, United States |
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| Abstract: | Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including generalized autoregressive conditional heteroskedastic (GARCH) models and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail thickness due to small sample bias. Thus, high quantile estimation may lead to a substantial underestimation of tail risk. |
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