In finance, a lattice model is a technique applied to the valuation bootstrapping yield curve investopedia forex derivatives, where a discrete time model is required. European value is the greater of this and the exercise value given the corresponding equity value. In general the approach is to divide time between now and the option’s expiration into N discrete periods. 1 is captured in a branch.
For equity and commodities the application is as follows. A variant on the Binomial, is the Trinomial tree, developed by Phelim Boyle in 1986, where valuation is based on the value of the option at the up-, down- and middle-nodes in the later time-step. Various of the Greeks can be estimated directly on the lattice, where the sensitivities are calculated using finite differences. When it is important to incorporate the volatility smile, or surface, Implied trees can be constructed. As regards the construction, for an R-IBT the first step is to recover the “Implied Ending Risk-Neutral Probabilities” of spot prices. Then by the assumption that all paths which lead to the same ending node have the same risk-neutral probability, a “path probability” is attached to each ending node.