Pricing Asian Options with Correlators

TL;DR

This paper introduces a Hermite polynomial series expansion method for pricing arithmetic Asian options, leveraging closed-form moments and correlators in polynomial jump-diffusions to enable explicit computation of Greeks without numerical simulation.

Contribution

It develops a novel Hermite polynomial series expansion approach for Asian options that uses closed-form moments in polynomial jump-diffusions, improving computational efficiency.

Findings

Series converges depending on the Gaussian scale parameter b.

Method provides accurate option prices and Greeks.

Numerical instability occurs for initial values far from zero.

Abstract

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This series requires the computation of moments and correlators of the underlying price process, but for a polynomial jump-diffusion, these are given in closed form, hence no numerical simulation is required to evaluate the series. This allows, for example, for the explicit computation of Greeks. The weight function defining the Hermite polynomials is a Gaussian density with scale $b$. We find that the rate of convergence for the series depends on $b$, 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.