Lattice Model

A discrete time model is needed when applying a lattice model to the valuation of derivatives. An example of a price equity option would be an American option, where option exercise decisions must be made at "all" times any time before and including maturity. On the other hand, a continuous model, like Black-Scholes, would only permit the valuation of European options, where the exercise date is the option's maturity date. Because they handle of many problems with continuous models, such as pull to par, lattices are also helpful for interest rate derivatives. The approach is also used to value some unusual options, for which Monte Carlo methods for option pricing do not account for the best choices to terminate the derivative by early exercise due to route dependency in the payout, despite the fact that solutions to this issue currently exist.