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

In this article, we generalize and analyse the model for pricing American-style Asian options proposed by Hansen and Jørgensen (2000) by including a continuous dividend rate q and a general method of averaging the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The first-order expansion in terms of <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ramf_a_547041_o_ilm0001.gif"/> </inline-formula> 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 non-local 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.