Method[ edit ] As above, the PDE is expressed in a discretized form, using finite differencesand the evolution in the option price is then modelled using a lattice with corresponding dimensions : time runs from 0 to maturity; and price runs from 0 to a "high" value, such that the option is deeply in or out of the money. The option is then valued as follows:  Maturity values are simply the difference between the exercise price of the option and the value of the underlying at each point.
Values at the boundaries - i. Here, using a technique such as Crank—Nicolson or the explicit method : the PDE is discretized per the technique chosen, such that the value at each lattice point is specified as a function of the value at later and adjacent points; see Stencil numerical analysis ; the value at each point is then found using the technique in question.
At the same time, like tree-based methods, this approach is limited in terms of the number of underlying variables, and for problems with multiple dimensionsMonte Carlo methods for option pricing are usually preferred.