Nonlinear VaR Model of Options Portfolio under Multivariate Mixture of Normals Distributions

Abstract

The paper proposes a kind of nonlinear VaR model of options portfolio under heavy-tailed market risk factors. The paper depicts heavy-tailed market risk factors using multivariate mixture of normals distribution, and derives the moment generating function that reflects the change in options portfolio value. Moreover, to make use of the relationship between characteristic function and moment generating function, the paper develops Fourier-Inversion method and adaptive Simpson rule with iterative algorithm of numerical integration into nonlinear VaR model of options portfolio, and calculates the VaR values of portfolio. Numerical results show that the VaR values using Fourier-Inversion method is slight difference from the VaR values using Monte Carlo simulation method. However, the calculation speed using Fourier-Inversion method is obviously quicker than the speed using Monte Carlo simulation method.