股市投资回报过程的长相依性与风险度量

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.

Long Range Dependence and VaR of Stock Return Process

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.