A General Approach to Compute Standard Risk Measures

This article focuses on the computation of VaR and CTE. It provides a very accurate and fast method, based on Fourier analysis and following Boyarchenko and Levendorskii (2000). Once the characteristic function of a marginal law is known, the computation of VaR or CTE is performed using a Fast Fourier Transform. We use different Levy processes, namely a Kou process and a CGMY process which are representative of processes with finite and infinite activity respectively. We also consider a specific regime switching model. We show the method accuracy and rapidity. The results are obtained instantaneously as if we had a closed form solution. We give as a synthesis of this method and as an illustration, the computations of VaR and CTE for a simplified variable annuities contract