  In this paper we consider Fourier transform techniques to efficiently compute
the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random
variable, characterized by having a computable generalized characteristic
function. We exploit the property of these risk measures of being the solution
of an elementary optimization problem of convex type in one dimension for which
Fast and Fractional Fourier transform can be implemented. An application to
univariate loss models driven by L\'{e}vy or stochastic volatility risk factors
dynamic is finally reported.
