Alternative statistical distributions for estimating value-at-risk: theory and evidence
A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student’s t and SGT distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student’s t and normal distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student’s t and normal distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student’s t) on VaR estimates in stock markets for a long position. Copyright Springer Science+Business Media, LLC 2012
Volume (Year): 39 (2012)
Issue (Month): 3 (October)
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- Robert F. Engle & Simone Manganelli, 2004.
"CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 22, pages 367-381, October.
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- Baillie, Richard T. & DeGennaro, Ramon P., 1990.
"Stock Returns and Volatility,"
Journal of Financial and Quantitative Analysis,
Cambridge University Press, vol. 25(02), pages 203-214, June.
- So, Mike K.P. & Yu, Philip L.H., 2006. "Empirical analysis of GARCH models in value at risk estimation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(2), pages 180-197, April.
- 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.
- Pierre Giot & Sébastien Laurent, 2003.
"Value-at-risk for long and short trading positions,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
- GIOT, Pierre & LAURENT, Sébastien, 2001. "Value-at-risk for long and short trading positions," CORE Discussion Papers 2001022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP 1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
- Chin, Wen Cheong, 2008. "Heavy-tailed value-at-risk analysis for Malaysian stock exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4285-4298.
- Ming-Chih Lee & Jung-Bin Su & Hung-Chun Liu, 2008. "Value-at-risk in US stock indices with skewed generalized error distribution," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 4(6), pages 425-431.
- Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2007. "A robust VaR model under different time periods and weighting schemes," Review of Quantitative Finance and Accounting, Springer, vol. 28(2), pages 187-201, February.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December.
- Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2010. "The Use of GARCH Models in VaR Estimation," Working Papers 0048, University of Peloponnese, Department of Economics.
- Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
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