一类金融时间序列VaR和CVaR的非参数计算

Nonparametric Computation of VaR and CVaR for a Type of Financial Series

该文在损益变化为一个严平稳过程的假设下,采用非参数方法给出了在已知t时刻之前的历史损益时,t时刻风险值估计所应满足的方程,以及条件风险值估计的解析表达式.以S&P500指数为实例,讨论了t时刻之前的历史损益数据长度对t时刻风险值和条件风险值的影响,并将算得的风险值与由GARCH模型得到的风险值进行了比较,发现它们反映风险随时间的波动情况基本一致,但该方法避免了正态假设,因此得到的风险值相对较大,变化也较平缓.最后,采取不同数量的样本对风险值进行估计,结果表明方法是稳健的.

Under the assumption that the yield series is a strictly stationary process, we present an equation satisfied by value at risk （VaR） at time t given historical data and an analytic formula for conditional value at risk （CVaR）. We use S＆P 500 as an example to discuss how the length of historical data before t affects the estimate of VaR and CVaR at time t. The VaR series obtained with the proposed method and that with the GARCH model are compared. It is found that both results have similar fluctuations, hut VaR values of the former is larger and smoother because normality assumption is not used. By using different sample length to estimate CVaR, the proposed method is shown to be more robust.