Dynamic value-at-risk models and the peaks-over-threshold method for market risk measurement: an empirical investigation during a financial crisis

Abstract

This paper presents a backtesting exercise involving several value-at-risk (VaR) models for measuring market risk in a dynamic context.The focus is on the comparison of standard dynamic VaR models, ad hoc fat-tailed models and the dynamic peaks-over-threshold (POT) procedure for VaR estimation with different volatility specifications. We introduce three different stochastic processes for the losses. Two of them are of the generalized autoregressive conditional heteroskedasticity type and one is of the exponentially weighted moving average (EWMA) type. In order to assess the performance of the models, we implement a backtesting procedure using the log losses of a diversified sample of fifteen financial assets. The backtesting analysis covers the period from March 2004 to May 2009, thereby including the subprime crisis. The results show that the POT approach and a dynamic historical simulation method, both combined with the EWMA volatility specification, are particularly effective at high VaR coverage probabilities and outperform the other models under consideration. Moreover, VaR measures estimated with these models react quickly to the turmoil of the last part of the backtesting period, so that they seem to be efficient in high-risk periods as well.