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.