2003/10/22 by Kamdem, Jules Sadefo
#Classical Analysis and ODEs (math.CA) #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #G.1.1 #G.1.10 #G.1.2 #G.1.9 #J.1 #J.2 #J.4 #and Science (cs.CE)
paper · doi:10.48550/arxiv.cs/0310043
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 contains 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 log-returns changes with multivariate elliptic distribution. 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 special attention to the mixture of normal and mixture of t-student distribution. For given VaR, when joint Risk Factors changes with elliptic distribution, we show how to estimate an Expected Shortfall .