VaR Estimation for Quadratic Portfolio of Securities with Mixture of Elliptic Distributed Risk Factors

Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contained derivatives instruments. In this paper, we postpone to estimate the Value-at-Risk of a quadratic portfolio of securities (i.e equities) without the Delta and Gamma greeks, when the joint underlying log-returns changes with multivariate elliptic distribution. By using numerical method of Alan Genz (2003) in [6], we have reduced the estimation of the quadratic VaR of such portfolio to a resolution of one dimensional integral equation. To illustrate our method, we give attention to mixture of normal distribution, and mixture of t-student distribution.