A Fourier Approach to the Computation of Conditional Value-at-Risk and Optimized Certainty Equivalents

Abstract

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as conditional value-at-risk (CVaR) and monotone mean–variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very competitive method for the calculation of CVaR, which is comparable in computational time to the calculation of VaR. We also develop methods for the efficient computation of risk contributions.

Keywords: conditional value-at-risk, Fourier approach, optimized certainty equivalents