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In this paper we consider Fourier transform techniques to efficiently computethe Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss randomvariable, characterized by having a computable generalized characteristicfunction. We exploit the property of these risk measures of being the solutionof an elementary optimization problem of convex type in one dimension for whichFast and Fractional Fourier transform can be implemented. An application tounivariate loss models driven by L\'{e}vy or stochastic volatility risk factorsdynamic is finally reported.

methodology and computing in applied probability

On a Transform Method for the Efficient Computation of Conditional VaR  (and VaR) with Application to Loss Models with Jumps and Stochastic  Volatility