Numerical Methods in Multivariate Option Pricing

Many numerical methods to price options have been suggested in the finance literature. This paper aims at reviewing several numerical approaches in order to discuss their practical strenghts and/or weaknesses. The problem under investigation is a multivariate contingent claims model with three underlying assets. We compare several alternatives in the partial differential equation framework: explicit, ADI, and implicit methods, the Fourier grid method, and the Monte Carlo approach, which becomes the only amenable method when the dimension of the problem grows. The comparison criteria are computational complexity, robustness with respect to initial conditions and parameter settings, and potential for a parallel implementation.