Endogenous Determination of Element Length on Financial Option Pricing with the Finite Element Method

Abstract

This study proposes an efficient version of the finite element method (FEM) in option pricing. In this study,we determine element lengths endogenously from the curvature of the Black-Sholes equation. In our method elements reconstruction of FEM consists of two algorithms, expansion of elements, and repartition of elements. We let elements be larger if the curvature of the local domain is low, and be smaller if it is high at each time step. We apply this method to one-dimensional options, a European up-and-out call option,and a compound option. As a result of numerical analysis, we verify that this method is able to reduce the experiment time, while the accuracy remains at a comparable level.