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Measuring Tail Thickness under GARCH and an Application to Extremal Exchange Rate Changes

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Author Info
Niklas Wagner (Munich University of Technology)
Terry Marsh (Haas School of Business, University of California, Berkeley)

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Abstract

Accurate modeling of extremal 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 GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly 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. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.

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File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1012&context=iber/finance
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Paper provided by Research Program in Finance, Institute for Business and Economic Research, UC Berkeley in its series Research Program in Finance, Working Paper Series with number 1012.

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Date of creation: 01 Jun 2003
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Handle: RePEc:cdl:rpfina:1012

Note: oai:cdlib1:iber/finance-1012
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Keywords: fat tails tail index stationary marginal distribution GARCH Hill estimator foreign exchange

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  1. Huisman, R. & Koedijik, K.G. & Pownall, R.A.J., 1998. "VaR-x: Fat Tails in Financial Risk Management," Papers 98-54, Southern California - School of Business Administration.
  2. ROCKINGER, Michael & JONDEAU, Eric, 1999. "The Tail Behavior of Stock Returns: Emerging versus Mature Markets," Les Cahiers de Recherche 668, Groupe HEC. [Downloadable!]
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  3. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  4. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May. [Downloadable!] (restricted)
  5. Vries, Caspar de & Danielsson, Jon, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH.
  6. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
  7. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  8. Michel M. Dacorogna, & Ulrich A. Muller & Olivier V. Pictet & Casper De Vries,, . "The Distribution of Extremal Foreign Exchange Rate Returns in Extremely Large Data Sets," Working Papers 1992-10-22, Olsen and Associates. [Downloadable!]
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