Estimating Option Prices with Discrete Dividend Payment Using Finite Difference Method and Monte Carlo Simulation: A Comparative Study

Md Joshem Uddin

Abstract: Valuation of the option prices through numerical methods and real option valuation has had a significant influence on the way the traders price the financial derivatives over the past years. The Black-Scholes (BS) model is an essential model that plays an important role in pricing option prices. In this paper, the numerical solution of the Black-Scholes model for pricing European call options with discrete dividend payment using the Monte Carlo (MC) and Finite-Difference Method (FDM) has been presented. The explicit, implicit, and Crank Nicolson finite difference schemes have been used in this study. All of these approaches, including MC Simulation, are applied to the same example to assess their efficiency. The results obtained using these methods have been compared to the option values derived using the option pricing formula. Numerical results reveal that the Crank Nicolson Finite Difference Scheme (CNFDS) converges faster and offers more accurate results than the other two Finite Difference Schemes (FDSs) and the MC simulation.