Lattices in option pricing

In binomial trees, each node recombines at every alternative node. In trinomial trees, each node recombines at every other node. This property of recombining trees can also be represented as lattices to save memory without recomputing and storing recombined nodes.

Using a binomial lattice

We will create a binomial lattice from the binomial CRR tree since at every alternate up and down nodes, the prices recombine to the same probability of ud=1. In the following diagram, S_u and S_d recombine with S_du = S_ud = S₀. The tree can now be represented as a single list:

For a N-step binomial tree, a list of size 2N +1 is required to contain the information on the underlying stock prices. For European...