Value-at-risk and extreme value distributions for financial returns

ABSTRACT The ability of the generalized extreme value (GEV) and generalized logistic (GL) distributions to fit extreme financial returns in the stock, commodities and bond markets is assessed. The empirical results indicate that the too much celebrated GEV is not the most appropriate model for the data since the fatter tailed GL is found to provide better descriptions of the extreme returns. Extreme value theory (EVT) based value-at-risk (VaR) estimates are then derived and compared with those generated by traditional methods. The results show that when the focus is on the really ruinous events, which are located deep into the tails of the returns distribution, the EVT methods used in this study can be particularly useful since they produce VaR estimates that outperform those derived by the traditional methods at high confidence levels. However, these estimates were found to be considerably higher than those derived by traditional VaR models, consequently leading to higher capital reserves for financial institutions.