Kernel Based Estimation of Spectral Risk Measures

Abstract

Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimator for the class of spectral risk measures (SRMs) has the form of L-statistics. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d cases and apply them to our kernel based estimator of SRM. We prove that the estimator is strongly consistent and asymptotically normal. We compare the finite sample performance of the kernel based estimator with that of empirical estimator of SRM using Monte Carlo simulation, where appropriate choice of smoothing parameter and the user's coefficient of risk aversion plays an important role. We estimate the exponential SRM of four future indices, namely, Nikkei 225, Dax, FTSE 100 and Hang Seng using our proposed kernel based estimator.