A numerical analysis of variational valuation techniques for derivative securities

In this paper, we consider the partial differential equations approach for valuing European and American style options on multiple assets. We use a method of lines finite element implementation available in the software package Femlab in order to solve the variational inequality that characterizes the American style option, as well as the partial differential equation that defines the European style option, for two and three state variables. A detailed study of the approximation error is provided, including a theoretical estimate, an asymptotic analysis, the space-time distribution, and the dependence on the size of the truncation domain.