Finite difference models

The equations used to model the option are often expressed as partial differential equations (see for example Black–Scholes PDE). Once expressed in this form, a finite difference model can be derived, and the valuation obtained. This approach is useful for extensions of the option pricing model, such as changing assumptions as to dividends, that are not able to be represented with a closed form analytic solution. A number of implementations of finite difference methods exist for option valuation, including: explicit finite difference, implicit finite difference and the Crank-Nicholson method. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method.