Comparison of Two Numerical Methods for Computation of American Type of the Floating Strike Asian Option

TL;DR

This paper introduces two novel numerical algorithms for solving the free boundary problem in pricing American floating strike Asian options, transforming the problem into a fixed domain and validating accuracy through computational experiments.

Contribution

The paper presents two new numerical algorithms, a predictor-corrector and a Newton-based method, for efficiently solving the free boundary problem in Asian option pricing.

Findings

Both algorithms accurately solve the free boundary problem.

Computational experiments confirm the effectiveness of the proposed methods.

Abstract

We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear time-dependent term is involved in the resulting equation. Two new numerical algorithms are proposed. In the first algorithm a predictor-corrector scheme is used. The second one is based on the Newton method. Computational experiments, confirming the accuracy of the algorithms are presented and discussed.