Bayesian Entropic Inverse Theory Approach to Implied Option Pricing with Noisy Data

Abstract

A popular approach to nonparametric option pricing is the Minimum Cross Entropy (MCE) method based on minimization of the relative Kullback-Leibler entropy of the price density distribution and a given reference density, with observable option prices serving as constraints. When market prices are noisy, the MCE method tends to overfit the data and often becomes unstable. We propose a non-parametric option pricing method whose input are noisy market prices of arbitrary number of European options with arbitrary maturities. Implied transition densities are calculated using the Bayesian inverse theory with entropic priors, with a reference density which may be estimated by the algorithm itself. In the limit of zero noise, our approach is shown to reduce to the canonical MCE method generalized to a multi-period case. The method can be used for a non-parametric pricing of American/Bermudan options with a possible weak path dependence.