Numerical valuation of Bermudan basket options via partial differential equations

TL;DR

This paper evaluates a PCA-based PDE approach for valuing Bermudan basket options, demonstrating its efficiency and second-order convergence through numerical experiments, with insights into irregular convergence behavior.

Contribution

It applies and analyzes a PCA-based PDE method for Bermudan basket options, highlighting its efficiency and convergence properties with detailed numerical validation.

Findings

Second-order convergence in space and time

Irregular convergence behavior observed

Method is computationally efficient

Abstract

We study the principal component analysis (PCA) based approach introduced by Reisinger & Wittum (2007) for the approximation of Bermudan basket option values via partial differential equations (PDEs). This highly efficient approximation approach requires the solution of only a limited number of low-dimensional PDEs complemented with optimal exercise conditions. It is demonstrated by ample numerical experiments that a common discretization of the pertinent PDE problems yields a second-order convergence behaviour in space and time, which is as desired. It is also found that this behaviour can be somewhat irregular, and insight into this phenomenon is obtained.