Kernel Based Estimation of Spectral Risk Measures
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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. In the literature, various authors have studied and derived the asymptotic properties of the estimator of SRM using the empirical distribution function. But no such estimator of SRM is studied considering distribution function estimator other than empirical cdf. We propose a kernel based estimator of SRM. We try to 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 the estimator is 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. Based on our simulation study we have estimated the exponential SRM of four future index-that is Nikkei 225, Dax, FTSE 100 and Hang Seng using our proposed kernel based estimator.
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