The ShortRateTree(M, G) calling sequence returns a trinomial tree approximating the stochastic process that represents the instantaneous spot rate in the given short-rate model. The constructed tree will be based on the time discretization given by G.

Assume that the time grid G consists of  points , , ..., . Then the resulting trinomial tree will have  levels, each level representing possible states of the discretized process at time , . At level ,  the tree has  nodes, , ..., , where  is the number of nodes at level  (see GetSize). Each node  has three descendants at level ,  (the upper descendant),  (the middle descendant) and  (the lower descendant). The initial state of the underlying process and the transition probabilities (i.e. the probability of going from  to , the probability of going from  to , and the probability of going from  to ) will be calculated based on the given model.

The ShortRateTree(M, T, N) calling sequence is similar except that in this case a uniform time grid with step size  is used instead of G.

The ShortRateTree(X, G) and ShortRateTree(X, T, N) commands construct a trinomial tree approximating an Ito process X. This tree is constructed using the procedure proposed by Hull and White [4], [5] (see also [1] and [2]). This construction requires that the diffusion term in the corresponding SDE is independent of the state variable X.

The Finance[ShortRateTree] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice, New York: Springer-Verlag, 2001.

Glasserman, P., Monte Carlo Methods in Financial Engineering, New York: Springer-Verlag, 2004.

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

Hull, J., and White, A., Numerical Procedures for Implementing Term Structure Models I: Single-Factor Models, Journal of Derivatives, 1994, 7-16.

Hull, J., and White, A., Using Hull-White Interest Rate Trees, Journal of Derivatives, 1996, 26-36.