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

Jeroen P. A. Devreese, Damiaan Lemmens, Jacques Tempere

Published 2009-06-24, updated 2011-09-23Version 3

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.