Kernel Based Estimation of Spectral Risk Measures

TL;DR

This paper introduces a kernel-based estimator for spectral risk measures, demonstrating its strong consistency, asymptotic normality, and superior finite sample performance over existing methods through simulation and real data applications.

Contribution

The paper proposes a novel kernel-based estimator for spectral risk measures and establishes its theoretical properties, outperforming existing estimators in simulations and practical applications.

Findings

Kernel estimator is strongly consistent and asymptotically normal.

Outperforms existing estimators in finite sample simulations.

Effectively estimates exponential SRM for major financial indices.

Abstract

Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical estimator of SRM. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d and dependent observations and apply them to our estimator. We prove that it is strongly consistent and asymptotically normal. We compare the finite sample performance of our proposed kernel estimator with that of several existing estimators for different SRMs using Monte Carlo simulation. We observe that our proposed kernel estimator outperforms all the estimators. Based on our simulation study we have estimated the exponential SRM of four future indices-that is Nikkei 225, Dax, FTSE 100, and Hang Seng. We also discuss the use of SRM in setting initial margin requirements of clearinghouses. Finally we perform a backtesting exercise of SRM.