Kernel-based estimation of spectral riskmeasures

Spectral risk measures (SRMs) belong to the family of coherent risk measures.A natural estimator for the class of SRMs takes the form ofL-statistics. Variousauthors have studied and derived the asymptotic properties of the empirical estima-tor of SRMs; we propose a kernel-based estimator. We investigate the large-sampleproperties of generalL-statistics based on independent and identically distributedobservations and dependent observations and apply them to our estimator. We provethat it is strongly consistent and asymptotically normal. Using Monte Carlo simu-lation, we compare the finite-sample performance of our proposed kernel estima-tor with that of several existing estimators for different SRMs and observe that ourproposed kernel estimator outperforms all the other estimators. Based on our sim-ulation study, we estimate the exponential SRM for heavily traded futures (that is,the Nikkei 225, Deutscher Aktienindex, Financial Times Stock Exchange 100 andHang Seng futures). We also discuss the use of SRMs in setting the initial-marginrequirements of clearinghouses. Finally, we perform an SRM backtesting exercise.