PRICING ASIAN OPTIONS with CORRELATORS

Abstract

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This requires the computation of moments and correlators of the underlying asset price which for a polynomial jump–diffusion process are given analytically; hence, no numerical simulation is required to evaluate the series. This allows to derive analytical expressions for the option Greeks. The weight function defining the Hermite polynomials is a Gaussian density with scale [Formula: see text]. We find that the rate of convergence of the series depends on [Formula: see text], for which we prove a lower bound to guarantee convergence. Numerical examples show that the series expansion is accurate but unstable for initial values of the underlying process far from zero, mainly due to rounding errors.