Path Integral and Asian Options

TL;DR

This paper develops an analytical method using path integrals and spectral expansion to price arithmetically averaged Asian options, providing a new approach in financial derivatives valuation.

Contribution

It introduces a novel path integral formalism with an effective action for Asian options, enabling analytical spectral expansion solutions.

Findings

Derivation of a spectral expansion formula for Asian options

Application of Feynman-Kac theorem in option pricing

Use of Bessel and Whittaker functions in the solution

Abstract

In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral is evaluated by use of the Feynman-Kac theorem. After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion for the value of Asian options.