Approximating Option Prices with Black Scholes using The Finite Element Method

Sammanfattning

This thesis investigates the use of the Finite Element Method (FEM) to numerically solve the Black-Scholes partial differential equation, a fundamental model in financial mathematics for option pricing. The primary objective is to evaluate how accurately FEM can approximate option prices compared to actual market data. Two European call options based on the S&P 500 Index were selected for analysis, and historical market data was used to validate the simulation results. The findings demonstrate that FEM provides reliable approximations of option prices, particularly during stable market conditions. However, significant deviations were observed when market volatility increased, highlighting the limitations of the simulation’s use of constant volatility.