Estimation of extreme value-at-risk: An EVT approach for quantile GARCH model

We proposed a method to estimate extreme conditional quantiles by combining quantile GARCH model of Xiao and Koenker (2009) and extreme value theory (EVT) approach. We first estimate the latent volatility process using the information of intermediate quantiles. We then apply EVT to the tail observations to obtain a sound estimate of the likelihood of experiencing an extreme event. Quantile autoregression and EVT together improve efficiency in estimation of extreme quantiles, by borrowing information from neighbor quantiles. Monte Carlo simulation indicates that, the proposed method is promising to provide more accurate estimates for VaR of a financial portfolio, where non-Gaussian tail is present.