A nonparametric copula approach to conditional Value-at-Risk

Value-at-Risk and its conditional allegory, which takes into account the available information about the economic environment, form the centrepiece of the Basel framework for the evaluation of market risk in the banking sector. A new nonparametric framework for estimating this conditional Value-at-Risk is presented. A nonparametric approach is particularly pertinent as the traditionally used parametric distributions have been shown to be insufficiently robust and flexible in most of the equity-return data sets observed in practice. The method extracts the quantile of the conditional distribution of interest, whose estimation is based on a novel estimator of the density of the copula describing the dynamic dependence observed in the series of returns. Monte-Carlo simulations and real-world back-testing analyses demonstrate the potential of the approach, whose performance may be superior to its industry counterparts.