Calibration and Comparison of Spectral Risk Measures for a 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 them 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 propose a methodology to both calibrate and compare SRMs. For that, we rely on concepts of relative entropy optimization allowing us first to build a data-implied distortion as a reference measure for calibration and second to define an entropic risk measure that we use for comparison. Finally, we apply the methodology to real market data and assess four SRM through various specifications of the historical probability measure.