基于样本外分布回测的随机过程统计推断方法

采用不同的随机过程模型描述标的资产的价格动态，会极大的影响衍生品定价和风险管理活动。在文献中，同一资产采用的随机过程往往是不一致甚至是矛盾的。本文以GBM过程与OU过程为例，提出了一种统计推断方法，旨在从多个备选模型中选出能更好的描述标的资产价格动态的随机过程。该方法应用事后检验原理，将数据分成估计窗和检验窗，估计窗用来估计随机过程的参数，然后在模型参数不变的假定下，推导了原假设成立时检验窗各个时点的资产价格的样本外分布，看实际数据落在接受域或拒绝域的频数来判断是否接受原假设。本文以大宗商品、汇率、利率、股票作为标的资产，对随机过程选择进行了实证分析。实证结果表明，一些经常使用的随机过程模型并不一定是最优的模型。

A Statistical InferenceApproach for the Selection of Stochastic Process Based on Back Testing of Out-of-sample Distribution

Derivative pricing and risk management are affected by the selection of stochastic process using to describe the asset price. In some literature, the stochastic processes of underlying asset are different, even inconsistent. In this article, a statistic inference approach is put forward to choose the best stochastic process to describe underlying asset from different processes. The approach uses the back testing. Firstly, it divides the data into estimation window and test window, then estimates the parameters of the stochastic process, finally, deduces the out of sample distribution of every asset price in test window under the assumption of fixed parameters. The win ratio about the real data falling on the accepting region is used to judge whether the null hypothesis is true or not. Commodity, exchange rate, interest rate and stock are used as underlying asset. The empirical results reveal that in some circumstance, commonly-used model describing the asset price is not optimal.