A Numerical Algorithm Based on a Fitted Finite Volume Method for Option Pricing with Its Implementation in Mathematica

Over the past years, financial valuation through numerical option pricing and real option valuation has played an important role to support sustainable development in commodity markets. Although many empirical evidences have revealed some drawbacks of the log-normal Black–Scholes model, it is an essential model that helps with the understanding of various methodologies while pricing financial derivatives. In this work, we consider a fitted finite volume discretization for pricing European options under the log-normal diffusion model of Black–Scholes. Unlike the finite difference method which is applied on the differential form of the pricing equation, the finite volume method leads to better stability and accuracy given that it is rather based on the integral form of the conservation laws. The implementation of the method under the Mathematica environment is described, and numerical comparisons with the finite difference method show the merit of the scheme.