Bayesian Analysis of Tail Asymmetry Based on a Threshold Extreme Value Model

This paper studies a threshold extreme value distribution for modeling standardized financial returns. 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 (1995) 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 we are concerned with the right tail of the return distribution, i.e. in the short position. Our method performs particularly well in 10-day-1% and 10-day-99% value at risk forecasting, which are Basel requirements for capital adequacy calculation