Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics

Abstract

We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.