Abstract: 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.

Key words: selection of stochastic process, statistical inference, model specification, model risk