In Chapter 3 we discussed various models where the stock process follows a stochastic differential equation (SDE). We discussed the theoretical solution of such equations, and when the solution exists we derived a formula for the vanilla option price.
In general, finding analytic formulas is complicated and often impossible. In this chapter we will present a general methodology to approximate the solution of an SDE with a discrete time, discrete state space process. We shall refer throughout this chapter to such approximating processes as trees. Specifically, the problem can be formulated in the following way.
Suppose we have a stochastic process solving the SDE:
where and are known function. The theory presented at the end of this chapter applies to ‐dimensional stochastic processes , not just one dimensional. Later in this chapter we shall present ...