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.

翻译：谱风险测度（SRMs）属于一致性风险测度族。该类SRMs的自然估计量具有L-统计量的形式。多位学者已研究并推导了SRM经验估计量的渐近性质。本文提出一种基于核的SRM估计量，研究基于独立同分布观测和相关观测的一般L-统计量的大样本性质，并将其应用于所提出的估计量。我们证明该估计量具有强相合性和渐近正态性。通过蒙特卡洛模拟，我们比较了所提出的核估计量与多种现有SRM估计量在有限样本下的表现，发现核估计量优于所有对比估计量。基于模拟研究，我们估计了日经225、德国DAX、富时100和恒生指数四种期货指数的指数型SRM。此外，本文讨论了SRM在清算所初始保证金设定中的应用，并最终对SRM进行了回溯测试。