Retrieving risk neutral densities based on risk neutral moments through a Gram–Charlier series expansion

Abstract

In this paper we employ a new method to retrieve the risk neutral probability density function of future asset prices, or their implied log-returns, based on an exponential form of a Gram–Charlier series expansion, known as C-type. This type of expansion guarantees that the values of the risk neutral density will be always positive and it can account for strong deviations of the stock price distributions from the Gaussian. In a set of numerical and empirical applications, the paper shows the accuracy and versatility of the method for recovering the true risk neutral density.