Path integral approach to Asian options in the Black-Scholes model

TL;DR

This paper introduces a path integral method to derive closed-form solutions for Asian option pricing in the Black-Scholes model, including variants with barriers and correlations, validated against Monte Carlo simulations.

Contribution

It presents a novel path integral approach for Asian options, providing exact and approximate pricing formulas that extend existing methods.

Findings

Closed-form solutions for geometric Asian options derived.

Comparison shows good agreement with Monte Carlo simulations.

New formulas for Asian options with barriers and correlation effects.

Abstract

We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.