Use Finite Difference method to price European, American and Bermudan options.
- solution domain
- grid construction
- terminal and boundary condition
- spatial and time discretization
- finite difference scheme
PDE
The finite difference scheme
Delta hedge portfolio inequality, if execution timing is wrong, the portfolio value would be less:
The American option inequality:
For call option, w=1, for put, w =-1:
When V > w(S-K), PDE becomes European style:
When V = w(S-K), PDE is:
The we have a simple form:
There are two ways:
American option PDE can be rewrite as a linear complementarity (LCP) problem as below.
Where
