一类金融时间序列VaR和CVaR的非参数计算

上海大学学报(自然科学版) ›› 2007, Vol. 13 ›› Issue (6): 720-725 .

一类金融时间序列VaR和CVaR的非参数计算

谢潇衡，何幼桦

上海大学理学院，上海 200444

收稿日期:2007-09-06 修回日期:1900-01-01 出版日期:2007-12-20 发布日期:2007-12-20
通讯作者: 何幼桦

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

XIE Xiao-heng,HE You-hua

School of Sciences, Shanghai University, Shanghai 200444, China

Received:2007-09-06 Revised:1900-01-01 Online:2007-12-20 Published:2007-12-20
Contact: HE You-hua

摘要/Abstract

摘要：

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.

关键词: 风险值, 核估计, 平稳过程的条件密度, 条件风险值

Abstract:

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, but 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.

Key words: conditional density of stationary process, conditional value at risk (CVaR), kernel estimate

value at risk (VaR)

谢潇衡;何幼桦. 一类金融时间序列VaR和CVaR的非参数计算[J]. 上海大学学报(自然科学版), 2007, 13(6): 720-725 .

XIE Xiao-heng;HE You-hua. Nonparametric Computation of VaR and CVaR 
for a Type of Financial Series[J]. Journal of Shanghai University（Natural Science Edition）, 2007, 13(6): 720-725 .

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