Predictability Information Criterion for Selecting Stochastic Pricing Models

Pricing models of derivative instruments usually fail to provide reliable results when risks rise and financial crises occur. More advanced stochastic pricing models try to improve the fitting results adding risk factors and/or parameters to the models, incurring the risk of overfitted results. Drawing on these observations, it is proposed a generalisation of the Akaike Information Criterion (AIC) suitable to evaluate forecasting power of alternative stochastic pricing models for any fixed arbitrary forecasting time-horizon. The Predictability Information Criterion (PIC) differs from the classical criteria for evaluating statistical models as it assumes that the random variable to study can (or cannot) be partially predictable, which makes it particularly suitable for studying stochastic pricing models coherently with the semimartingale definition of the price process. On the basis of this assumption the criterion measures and compares the uncertainty of the predictions of two different alternative models when prices are (or are not) predictable. We conclude with a focus on the crude oil market by comparing GBM and OU stochastic processes that are commonly used for modeling West Texas Intermediate (WTI) oil spot price returns in derivative pricing models.