PDE, Finite Difference, and Black-Scholes Model

This is the book's second chapter of Part 3, and here we discuss a numerical method of solving partial differential equations (PDE) – the finite difference method (FDM) and solving the Black-Scholes PDE with it. PDEs are essential parts of financial engineering and have a significant role in determining derivatives like options. You may wonder why now; being a prerequisite, this should have been discussed in Part 1, but as it is very specific to options, I thought of doing the same here in Part 3. You may also take this chapter as a general discussion to learn methods of numerically solving PDEs, irrespective of the finance domain. We will try to keep our conversations as generic and independent as possible, though Black-Scholes PDE at the end will complete the circle of discussion being specific to financial engineering.