Numerical study of splitting methods for American option valuation

TL;DR

This paper compares the numerical efficiency and accuracy of three modern splitting methods and the penalty approach for valuing American options governed by partial differential complementarity problems.

Contribution

It provides a comprehensive numerical analysis of the convergence and accuracy of splitting methods for American option valuation.

Findings

Peaceman-Rachford method shows strong convergence properties.

Splitting methods' accuracy is comparable to the penalty approach.

Numerical experiments highlight the efficiency of modern splitting techniques.

Abstract

This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explicit payoff approach, the Ikonen-Toivanen approach and the Peaceman-Rachford method. In addition, the temporal accuracy of these splitting methods is compared to that of the penalty approach.