Application of Lie Symmetry method in pricing Arithmetic Asian options

Abstract

This research investigates the application of Lie symmetry method to find analytic solutions for arithmetic Asian options, which are crucial financial derivatives for managing risk in various commodity markets. By employing a two state partial differential equation approach, the study uses Lie symmetry method to enhance option pricing models. The research involves finding determining equations, infinitesimal generators, and invariant solutions, as well as examining the influence of parameters such as volatility, interest rates, and time on option prices.