An application of finite elements to option pricing

This study applied the finite element method (FEM) to pricing options. The FEM estimates the function that satisfies a governing differential equation through the assembly of piecewise continuous functions over the domain of the problem. Two common representations, a variational functional representation, and a weighted residual representation are used in the application of the method. The FEM is a versatile alternative to other popular lattice methods used in option pricing. Advantages include the abilities to directly estimate the Greeks of the option and allow nonuniform mesh construction. As an illustration of the advantages that the FEM offers, the method was used to price European put options and discrete barrier knock‐out put options. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:19–42, 2001