Solving the Black-Scholes Partial Differential Equation via the Solution Method for a One-Dimensional Heat Equation: A Pedagogic Approach with a Spreadsheet-Based Illustration

Abstract

The derivation of the Black-Scholes option pricing model, if covered in detail, is by far the most complicated among all major models in the finance curriculum. This paper presents a pedagogic approach to solve the Black-Scholes partial differential equation via the solution method for a one-dimensional heat equation. It is intended to help finance students with backgrounds in traditional business disciplines strengthen their understanding of the model derivation, without being distracted by the advanced mathematical requirements. Excel plays an important pedagogic role in this paper. The Excel illustration here not only confirms numerically some key features of the model derivation, but also connects the derived Black-Scholes formula and results from two key intermediate steps in the model derivation, thus making the analytical materials involved much easier to follow.