系统风险Beta系数的非参数估计

The Nonparametric Estimation of the Systemetic Risk (Beta Coefficient)

关于系统风险（Ｂｅｔａ系数）对时间的非平稳性己得到广泛的认可，但对Ｂｅｔａ系数的估计方法大都是在平稳的（或局部平稳）前提下，或者事先给定Ｂｅｔａ系数一个主观参数模型下进行的．本文假定证券价格或收益是一个连续时间的随机过程（时齐Ｉｔｏ过程），给出了过程的均值函数和协方差函数的同时非参数估计．把此结果应用到Ｂｅｔａ系数上，得到了Ｂｅｔａ系数的非参数估计．

Although the instability of systemetic risk has been commonly recognized, the beta coefficient of the market model was often estimated under the hypothesis of stability (or local stability), or was estimated by allowing beta to follow a fixed parametric model. By supposing the price or return of an asset is a random process, we give the nonparametric estimation of the mean and covariance function. And use these result, we get the nonparametric estimation of beta coefficient.