Chapter 4. Numerical Procedures

A derivative is a contract whose payoff depends on the value of some underlying asset. In cases where closed-form derivative pricing may be complex or even impossible, numerical procedures excel. A numerical procedure is the use of iterative computational methods in attempting to converge to a solution. One such basic implementation is a binomial tree. In a binomial tree, a node represents the state of an asset at a certain point of time associated with a price. Each node leads to two other nodes in the next time step. Similarly, in a trinomial tree, each node leads to three other nodes in the next time step. However, as the number of nodes or the time steps of trees increase, so do the computational resources consumed. Lattice pricing attempts to solve this problem by storing only the new information at each time step, while reusing values where possible.

In finite difference pricing, the nodes of the tree can also be represented as a grid. The...