A master equation approach to option pricing

TL;DR

This paper introduces a novel master equation framework for option pricing, modeling the underlying stochastic process at a mesoscopic level, and demonstrates its efficiency through simulations of European and American options.

Contribution

It presents a new mesoscopic stochastic approach to solve option pricing models, bridging microscopic dynamics with macroscopic equations.

Findings

Efficient numerical solution for European and American options

Successful stochastic simulation demonstrating approach viability

Potential for improved computational methods in option pricing

Abstract

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option price variable. The dynamics of the latter is constructed and formulated in terms of a master equation. The numerical efficiency of the approach is demonstrated by means of stochastic simulation of the mesoscopic process for both European and American options.