Financial Simulation Modeling in Excel

APPENDIX A

Partial Differential Equations

The foundation for many interest rate and derivative pricing models in finance starts with a partial differential equation (PDE). To understand how a model, such as the Black-Scholes Model, is formulated, one must first understand what a partial differential equation is and what is meant by a “solution” to such an equation. This text will assume the reader already has some familiarity with basic calculus. Furthermore, we will not go into extreme detail on the various methods by which a PDE is solved. This is a very complicated process, and entire mathematical books are written to deal with this specific problem. Instead we will only introduce the concept of “equation” and “solution” so that the meaning of these terms is clear when discussing financial theory.