4.4 Methods for European options: finite differences (FD)

The difficulty of extending analytical derivations much further motivates developments of computational tools, which calculate the fair value of an option directly with a computer. Finite differences are commonly used, because it is relatively simple to formulate and implement an algorithm that converges to the solution. In this section, we will see that the simplest form results in explicit 2-levels schemes that remain of limited practical interest. Rather than extending the theory with the so-called implicit methods, we will wait to develop a more general framework in chapter 5, and show how the implicit Crank-Nicholson method with finite differences is in fact a special case of a more general and more robust formulation using finite elements.

• 4.4.1 Naive implementation using financial variables
• 4.4.2 Improved scheme using log-normal variables