On a determination formula for the estimation of copula-based Value at Risk

Abstract

Value at Risk (VaR) is one of well employed risk measures in quantitative risk management in finance and insurance. In this paper, we deal with the estimate of VaR for the portfolio problem. The portfolio we consider consists of two risk variables, which are assumed not necessarily to be independent but possibly nonlinearly related; the relation is described by a copula function. As well known, copula provides a flexible tool to treating a nonlinear dependence among random variables. We are thus concerned with the estimate of copula-based VaR. A determination formula for this copula-based VaR is derived, which does not involve the copula density and is ready to be computed. Empirical study shows that the established formula works fairly well.