Entropy-Based Analysis of Spectral Risk Measures for Practical Implementation

Abstract

Recently, new coherent, law-invariant and comonotonic additive risk measures known as spectral risk measures (SRM) have been proposed as interesting complements to the regulatory-standard VaR. While such risk measures allow various attitudes towards risk to be specified by the risk manager through a risk spectrum, there has not been proposed to date any practical way of calibrating it but arbitrarily. It is not clear neither how a risk manager could supplement VaR or CVaR with such risk measures in its risk assessment process through a realistic methodology. In this paper, we provide a new methodology to both choose the best SRM, in the sense of closeness to the data-implied distortion which we introduce, and the a minima parameter to calibrate it in order to estimate (tail) risk beyond VaR. We also define a new tail risk measure as a relative-entropy-weighted average of SRMs which, beyond being coherent, is data-dependent. Finally, we apply the methodology to various classes of assets (equity, interest rate, foreign exchange) and assess four SRM through a back-testing procedure.