Alternating implicit direction methods for option pricing

Finite difference methods, of explicit and implicit kind, are presented to solve numerically the Black–Scholes partial differential equation in order to price financial options. Different kinds of stability and consistency analysis are introduced. Then, the same approach is adapted to the increasing complexity of the Heston partial differential equation, which has one more spatial dimension. Alternating direction implicit schemes are the tool that allows handling this new dimension with great time efficiency, without giving up on accuracy. Consistency is proved and recent results and conjectures on stability are presented.

This seminar concerns the results of Ariel’s MSc thesis.