Max VaR for non-normal and heteroskedastic returns

Abstract

In this work we propose Monte Carlo simulation models for dynamically computing MaxVaR for a financial return series. This dynamic MaxVaR takes into account the time-varying volatility as well as non-normality of returns or innovations. We apply this methodology to five stock market indices. To validate the proposed methods we compute the number of MaxVaR violations and compare them with the expected number. We also compute the MaxVaR-to-VaR ratio and find that, on average, dynamic MaxVaR exceeds dynamic VaR by 5-7% at the 1% significance level, and by 12-14% at the 5% significance level for the selected indices.