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Bayesian analysis of tail asymmetry based on a threshold extreme value model

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  • So, Mike K.P.
  • Chan, Raymond K.S.

Abstract

A threshold extreme value distribution for modeling standardized financial returns is investigated. The main theme is tail asymmetry, which means that the left and right tails of the standardized return distribution are not identical. The peak-over-threshold idea in extreme value theory is adopted to construct the threshold extreme value distribution with two generalized Pareto tails for modeling tail asymmetry. The estimation of unknown parameters is performed within the Bayesian paradigm. Bayesian tail asymmetry tests are set up and Chib’s marginal likelihood approach is found to be most reliable. In the empirical analysis of nine securities, strong evidence of tail asymmetry is observed in equities, whereas modest evidence is documented in currencies and Gold futures. Oil futures is very volatile but shows weak evidence of tail asymmetry. Equity indices show a thinner than normal right tail in volatile periods, contradicting the usual fat-tail assumption in financial return modeling. One striking result is that all securities exhibit an increasing propagation of tail asymmetry during financial crises, suggesting that the level of tail asymmetry can be an indicator of the occurrence of extreme financial events. In terms of risk calculation, the threshold extreme value distribution is superior to its symmetric version and Student’s t distribution in forecasting multiple-period value at risk, especially when the right tail of the return distribution, i.e. in the short position, is of interest. The proposed method performs particularly well in 10-day-1% and 10-day-99% value at risk forecasting, which are Basel requirements for capital adequacy calculation.

Suggested Citation

  • So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
  • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:568-587
    DOI: 10.1016/j.csda.2013.02.008
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    1. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55.
    2. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    3. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    4. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    5. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    6. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
    7. Turan G. Bali, 2007. "An Extreme Value Approach to Estimating Interest-Rate Volatility: Pricing Implications for Interest-Rate Options," Management Science, INFORMS, vol. 53(2), pages 323-339, February.
    8. Congdon, Peter, 2006. "Bayesian model choice based on Monte Carlo estimates of posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 346-357, January.
    9. Francesco Lisi, 2007. "Testing asymmetry in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 687-696.
    10. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    11. Mike K. P. So & Chi-Ming Wong, 2012. "Estimation of multiple period expected shortfall and median shortfall for risk management," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 739-754, March.
    12. Matteo Grigoletto & Francesco Lisi, 2009. "Looking for skewness in financial time series," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 310-323, July.
    13. Massimo Guidolin & Allan Timmermann, 2008. "International asset allocation under regime switching, skew, and kurtosis preferences," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 889-935, April.
    14. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    15. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    16. Chen, Cathy W.S. & So, Mike K.P., 2006. "On a threshold heteroscedastic model," International Journal of Forecasting, Elsevier, vol. 22(1), pages 73-89.
    17. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    18. Xin Zhao & Carl Scarrott & Les Oxley & Marco Reale, 2010. "Extreme value modelling for forecasting market crisis impacts," Applied Financial Economics, Taylor & Francis Journals, vol. 20(1-2), pages 63-72.
    19. Fabrizio Laurini & Jonathan Tawn, 2009. "Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 146-169.
    20. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
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