A Computational Analysis of the Black - Scholes Equations by Yifan Wang Alessandro

A Computational Analysis of the Black-Scholes Equations by Yifan Wang This paper explores the most decorated option pricing model in recent history of the financial industry: the Black-Scholes Equation. We will first study the framework of the Black-Scholes Equation in detail by introducing its object of evaluation, distinguished assumptions, and deduction of the Black-Scholes partial differential equation. Although Black and Scholes(1973) has proposed the famous Black-Scholes formula to evaluate the European option, the PDE form has proposed struggle in finding the exact analytical solution, thus giving rise to the enormous interest in the numerical approach. In the second part of this paper, we will introduce three primary numerical and simulation methods including Finite Element Method(FEM), Finite Difference Method(FDM) and Monte Carlo Simulation(MC). We will discuss extensively about each method and present its advantages and shortcomings. In general, FEM are better founded mathematically on extensive theoretical analysis. Nevertheless, FDM and MC can have some advantages, in particular in terms of the easiness of implementation. We will consider some of these aspects in the present paper. A Computational Analysis of the Black-Scholes Equations