Option Pricing with Aggregation of Physical Models and Nonparametric Statistical Learning∗

Financial models are largely used in option pricing. These physical models capture several salient features of asset price dynamics. The pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches, that empirically learn and correct pricing errors through estimating state price distributions. In this paper, we propose a new semiparametric method for estimating state price distributions and pricing financial derivatives. This method is based on a physical model guided nonparametric approach to estimate the state price distribution of a normalized state variable, called the Automatic Correction of Errors (ACE) in pricing formulae. Our method is easy to implement and can be combined with any model based pricing formula to correct the systematic biases of pricing errors and enhance the predictive power. Empirical studies based on S&P 500 index options show that our method outperforms several competing pricing models in terms of predictive and hedging abilities.