Lattice model (finance)

In finance, a lattice model^[1] is a mathematical approach to the valuation of derivatives in situations requiring a discrete time model. For dividend paying equity options, a typical application would correspond to the pricing of an American-style option, where a decision to exercise is allowed at any time up to the maturity. A continuous model, on the other hand, such as the standard Black–Scholes one, would only allow for the valuation of European options, where exercise is limited to the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par.^[2] The method is also used for valuing certain exotic options, because of path dependence in the payoff. Traditional Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise,^[3] but some methods now exist for solving this problem.