Numerical valuation of American basket options via partial differential complementarity problems

TL;DR

This paper compares two approximation methods for American basket options using low-dimensional PDCPs and introduces an efficient discretisation technique that improves convergence.

Contribution

It evaluates and compares principal component analysis and comonotonic approaches, and proposes a new discretisation method for better convergence in PDCP solutions.

Findings

Both methods produce similar approximations.

The new discretisation enhances convergence behavior.

Numerical experiments confirm the effectiveness of the approaches.

Abstract

We study the principal component analysis based approach introduced by Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali & Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.