EXHIBIT 1. The Grid/Rectangular Lattice
This exhibit defines the state space for the underlying process over the first two discrete time periods. The starting state at valuation date 0 is the single root of the lattice. At each date the underlying process is discretized into a number of vertical nodes/states indexed by j. The value denotes the underlying process in state j at date . The node , for instance, can evolve to any discrete state in with certain transition probabilities. For a Brownian motion, the transition probability can be easily determined by (25).