A penalty method for imposing continuously applied constraints will be presented. The penalty method can be used to impose barriers and early-exercise features. A flux-limiting scheme that handles degenerate pricing problems will be discussed. A finite element method that uses triangular elements for the solution of two-factor option pricing problems will also be presented. The finite element approach can improve computational efficiency and can support irregular domains.
Irregular domains occur when certain continuous lookback or two-asset barrier options are priced.