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definition - Lattice model (finance)

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Lattice model (finance)

                   
For other meanings, see lattice model (disambiguation)

In finance, a lattice model can be used to find the fair value of a stock option; variants also exist for interest rate derivatives.

The model divides time between now and the option's expiration into N discrete periods. At the specific time n, the model has a finite number of outcomes at time n + 1 such that every possible change in the state of the world between n and n + 1 is captured in a branch. This process is iterated until every possible path between n = 0 and n = N is mapped. Probabilities are then estimated for every n to n + 1 path. The outcomes and probabilities flow backwards through the tree until a fair value of the option today is calculated.

The simplest lattice model for options is the binomial options pricing model, while a more sophisticated variant is the Trinomial tree. For multiple underlyers multinomial lattices [1] can be built, although the number of nodes increases exponentially with the number of underlyings. For Interest rate derivatives the lattice is built by discretizing a short rate model, such as Hull-White or Black Derman Toy, or a forward rate-based model such as the LIBOR market model or HJM.

   
               

 

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