Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application

Abstract

On the basis of a sample of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, and for any small level q, the value-at-risk (VaR) at the level q, i.e. the size of the loss that occurs with a probability q, is estimated by new semi-parametric reduced-bias procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p an adequate real number. After a brief reference to the asymptotic properties of these new VaR-estimators, we proceed to an overall comparison of alternative VaR-estimators, for finite samples, through large-scale Monte-Carlo simulation techniques. Possible algorithms for an adaptive VaR-estimation, an application to financial data and concluding remarks are also provided.