股市投资回报过程的长相依性与风险度量  

Long Range Dependence and VaR of Stock Return Process

作　　者：徐林[1] 祝东进[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《经济数学》2013年第1期50-53,共4页Journal of Quantitative Economics

基　　金：国家自然科学基金项目(11126238;11201006);教育部人文社会科学项目(12YJC910012);安徽省高等学校自然科学基金重大项目(KJ2012ZD01);安徽省哲学社会科学规划项目(AHSK11-12D128)

摘　　要：对上证指数对数收益率的长相依性进行了统计检验并完成了相应的统计建模以及参数估计.通过选择分数布朗运动作为刻画股票投资回报的驱动过程,并得到了此模型下股指收益的VaR计算的显式表达式.数值分析的结果显示分数布朗运动模型下的VaR值要高于Black-Scholes模型下的VaR值,这表明长相依性质对于股指风险有很大的影响,在相关的金融风险产品的风险度量中应加以重视.This paper studied the long range dependence in Shanghai Composite Index, and finished statistical modeling for the corresponding financial data. The investment return of stock market was assumed to be driven by Fractional Brownian motion, and the VaR for the corresponding model was derived. Numerical examples were given to illustrate the impact of the long range dependence on VaR by comparing VaR under fractional Brownian motion model with the one under Black-Scholes model. Numerical results show that the long range dependence impacts greatly on the risk measure of financial derivatives relevant to equity index.

关 键 词：长相依性 R S统计量 分数布朗运动 在险价值 

分 类 号：F224[经济管理—国民经济]