金融风险管理中ES度量的非参数方法的比较及其应用

Nonparametric estimation and comparative analyses of ES in risk measure with applications

预期不足(ES)是近几年发展起来的用于测量和控制金融风险的量化工具.在金融时间序列中,将两步核估计应用于两步ES非参数估计之中,得到了ES模型的两步核光滑估计.通过计算其期望和方差,比较了两步核光滑ES估计与ES完全经验估计及一步核光滑估计的优劣,得到了有趣的结论:与VaR模型不同,两步光滑化并不能减小ES估计的方差,反而会增大其方差,并通过计算机模拟证实了理论获得的结论.对国内沪深两市中的封闭式基金进行了实证分析,计算了样本基金的ES完全经验估计、一步核光滑估计和两步核光滑估计,并计算了样本基金基于周收益率和ES的两步核光滑估计的风险调整收益(RAROC),以此对样本基金的业绩做出了评价.实证分析表明:在不同的置信水平下,基于周收益率和ES计算的风险调整收益排名比基于周收益率和VaR计算的风险调整收益排名要更加稳定.

Expected shortfall（ES） model developed recently is a powerful mathematical tool to measure and control financial risk.In this paper,two-step kernel smoothed processes are used to develop a two-step nonparametric estimator of ES.Comparisons between the proposed two-step kernel smoothed ES estimator to the existing fully empirical ES estimator and one-step kernel smoothing ES estimator were made by calculating expectation and variance of them.It is of great interest that the proposed two-step kernel smoothed ES estimator has been shown to increases the variance,totally different from the existing result that the kernel smoothed VaR estimator can produces reduction in both the variance and the mean square error.In addition,the simulation results conform to the theoretical analysis.In the related empirical analysis,the close-ended funds in Shanghai and Shenzhen stock markets were explored to compute the empirical ES estimates and kernel smoothing ES estimates for risk analysis.And the RAROC of the funds sample based on weekly return and ES were computed to make the performance evaluation of the funds. The empirical results show that,with weekly return,the method based on ES is higher reliability than those based on VaR.