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).