Early Exercise Boundary for American Type of Floating Strike Asian Option and Its Numerical Approximation

Abstract

In this paper we generalize and analyze the model for pricing American-style Asian options due to Hansen and Jorgensen 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 are presented.