Asymptotic Expansion of Risk-Neutral Pricing Density

Abstract

A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is approximated by using a complete set of orthogonal Hermite-polynomials. The derived model is calibrated and tested on a collection of 1075 European-style 'Deutscher Aktienindex' (DAX) index options and is shown to generate very precise option prices and a more accurate implied volatility surface than conventional methods.