Finite Elements Solutions to the Black - Scholes Equation

Abstract

Nowadays, for the financial industry it is important to implement mathematical tools of the advanced level. World’s well-known economists Fischer Black and Myron Scholes introduced the distinguished equation for option pricing in 1973. This Capstone project aims to find finite element solutions to the Black-Scholes Equation. For this, the Black-Scholes Equation is solved as a convection dominated problem through the Local Projection Stabilization, where Galerkin finite element method is applied to the parabolic equation. Hence, for the Local Projection Stabilization, the functions of L2 – orthogonal finite element basis of arbitrary order are constructed. These functions result in a diagonal mass matrix which are useful for time discretization.