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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.

**Subsections**