The BlackScholesBinomialTree(, r, d, v, G) calling sequence returns a binomial tree approximating a Black-Scholes process with the specified parameters. When r, d, and v are constant and the time grid is homogeneous, the BlackScholesBinomialTree constructs the standard Cox, Ross, and Rubinstein binomial tree. In the general case the binomial tree is constructed as follows:

Assume that the time grid G consists of  points , , ..., . Then the resulting binomial tree will have  levels, each level representing possible states of the discretized process at time , . At level ,  the tree has  nodes, , ..., . The initial state of the discretized process will be equal to . Each node  has two descendants at level ,  (the upper descendant), and  (the lower descendant), where  and . Note that the value of the local volatility must be independent of the value of the underlying process.

The transition probabilities  (the probability of going from  to ) and  (the probability of going from  to ).

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

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

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

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