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 we have to decide how many steps we are modeling (*n*); that is, how many steps the time to maturity of the option will be divided into. Alternatively, we can determine the length of one time step
*t,* (measured in years) on the tree:

If we know the volatility (*σ*) of the underlying, the parameters *u* and *d* are determined according to the following formulas...