In a recombining binomial model with n periods,the number of outcomes is n + 1.

Question

Quizplus · Accepted Answer

In a recombining binomial model with n periods, the number of outcomes is equal to the number of nodes in the tree. This is equal to the number of possibilities for the stock price at the end of each period, which is 2 (either up or down). So, there are 2 outcomes for the first period, 4 for the second (2 up and 2 down from the previous node), 8 for the third, and so on. Therefore, the total number of outcomes is 2^n. Adding the initial node (representing the initial stock price), the total number of nodes/outcomes is n + 1.

In a Recombining Binomial Model with N Periods,the Number of Outcomes