The Cox-Ross-Rubinstein model
The Cox-Ross-Rubinstein (CRR) model (Cox, Ross and Rubinstein, 1979) assumes that the price of the underlying asset follows a discrete binomial process. The price might go up or down in each period and hence changes according to a binomial tree illustrated in the following plot, where u and d are fixed multipliers measuring the price changes when it goes up and down. The important feature of the CRR model is that u=1/d and the tree is recombining; that is, the price after two periods will be the same if it first goes up and then goes down or vice versa, as shown in the following figure:
To build a binomial tree, first ...
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