Early exercise boundary for American type of floating strike Asian option and its numerical approximation

TL;DR

This paper extends the model for American-style Asian options by incorporating dividend rates and averaging methods, analyzing the early exercise boundary, and proposing an efficient numerical algorithm with comparative results.

Contribution

It introduces a generalized model with dividend rates and averaging methods, and develops a novel numerical algorithm for the early exercise boundary.

Findings

First order Taylor expansion near expiry

Efficient numerical algorithm based on front fixing method

Comparative analysis with existing methods

Abstract

In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate $q$ and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The first order Taylor series expansion of the early exercise boundary close to expiry is constructed. We furthermore propose an efficient numerical algorithm for determining the early exercise boundary position based on the front fixing method. Construction of the algorithm is based on a solution to a nonlocal parabolic partial differential equation for the transformed variable representing the synthesized portfolio. Various numerical results and comparisons of our numerical method and the method developed by (Dai and Kwok 2006) are presented.