Sensitivity analysis of the early exercise boundary for American style of Asian options

TL;DR

This paper develops a numerical method to analyze how the early exercise boundary of American Asian options depends on model parameters, considering different averaging methods and their impact on the option's optimal exercise strategy.

Contribution

It introduces an efficient numerical algorithm for free boundary problems in American Asian options and studies the sensitivity of the early exercise boundary to various parameters.

Findings

Early exercise boundary varies with averaging methods

Numerical algorithm effectively solves non-local PDEs

Sensitivity of boundary to model parameters quantified

Abstract

In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying asset prices over some predetermined time interval. The mathematical model for the option price leads to a free boundary problem for a parabolic partial differential equation. Applying fixed domain transformation and transformation of variables we develop an efficient numerical algorithm based on a solution to a non-local parabolic partial differential equation for the transformed variable representing the synthesized portfolio. For various types of averaging methods we investigate the dependence of the early exercise boundary on model parameters.