Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems

Abstract

We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and 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.

Keywords

• American basket option
• partial differential complementarity problem
• principal component analysis
• comonotonicity
• discretisation
• convergence