Numerical valuation of Bermudan basket options via partial differential equations

Abstract

We study the principal component analysis (PCA) based approach introduced by Reisinger and Wittum [Efficient hierarchical approximation of high-dimensional option pricing problems, SIAM J. Sci. Comp. 29 (2007), pp. 440–458] 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.

Keywords:

• Bermudan basket options
• principal component analysis
• finite differences
• ADI scheme
• stability
• convergence.

2010 Mathematics Subject Classifications:

• 65L05
• 65N06
• 91G60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 This is to be distinguished from the von Neumann stability analysis that is relevant only to normal matrices.