Schemes#

The Black-Scholes equation on a grid: explicit, implicit and Crank-Nicolson time stepping, the tridiagonal solves they need, the transformation to the heat equation, the link to trinomial trees, and knock-out barriers.

Crank-Nicolson

Crank-Nicolson

Laasonen’s implicit scheme

Laasonen's implicit scheme

The Thomas algorithm

The Thomas algorithm

Black-Scholes as the heat equation

Black-Scholes as the heat equation

Schwartz: explicit finite differences

Schwartz: explicit finite differences

Brennan-Schwartz: explicit schemes are trinomial trees

Brennan-Schwartz: explicit schemes are trinomial trees

Zvan-Forsyth-Vetzal barrier options

Zvan-Forsyth-Vetzal barrier options