Mastering Python for Finance - Second Edition

Pricing American options with finite differences

So far, we have priced European options and exotic options. Due to the probability of an early exercise nature in American options, pricing such options is less straightforward. An iterative procedure is required in the implicit Crank-Nicolson method, where the payoffs from earlier exercises in the current period take into account the payoffs of an earlier exercise in the prior period. The Gauss-Siedel iterative method is proposed in the pricing of American options in the Crank- Nicolson method.

Recall that in Chapter 2, The Importance of Linearity in Finance, we covered the Gauss-Siedel method of solving systems of linear equations in the form of Ax=B. Here, the matrix A is decomposed into ...