Managing the extremes : An application of extreme value theory to financial risk management

We compare the traditional GARCH models with a semiparametric approach based on extreme value theory and find that the semiparametric approach yields more accurate predictions of Value-at-Risk (VaR). Using traditional parametric approaches based on GARCH and EGARCH to model the conditional volatility, we calculate univariate one-day ahead predictions of Value-at-Risk (VaR) under varying distributional assumptions. The accuracy of these predictions is then compared to that of a semiparametric approach, based on results from extreme value theory. For the 95% VaR, the EGARCH’s ability to incorporate the asymmetric behaviour of return volatility proves most useful. For higher quantiles, however, we show that what matters most for predictive accuracy is the underlying distributional assumption of the innovations, where the normal distribution falls behind other distributions which allow for thicker tails. Both the semiparametric approach and the conditional volatility models based on the t-distribution outperform the normal, especially at higher quantiles. As for the comparison between the semiparametric approach and the conditional volatility models with t-distributed innovations, the results are mixed. However, the evidence indicates that there certainly is a place for extreme value theory in financial risk management