Option Pricing with Aggregation of Physical Models and Statistical Learning

Abstract

Financial mathematical models are useful tools for option pricing. These physical models provide a good first order approximation to the underlying dynamics in the financial market. Their pricing performance can be significantly enhanced when they are combined with statistical learning approaches, which empirically learn and correct pricing errors through estimating state price densities. In this paper, we propose a new semiparametric technique for estimating state price densities and pricing financial derivatives. This method is based on a semiparametric approach to estimating the survivor function of a normalized state variable and is easy to implement. Our method 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 ability.