Here’s a spreadsheet which calculates call and put prices using the CRR framework for n = 1, 2, 3, and 4 timesteps. For discussion of this method, see pp. 9-11 of http://fin4335.garven.com/fall2018/lecture15.pdf lecture note which we covered in class yesterday.
The key idea here involves determining option payoffs without having to recreate the entire stock binomial tree which is shown on page 9 of the above referenced lecture note. The way this is done involves determining for each call option the minimum number of up moves required in order to determine the nodes at which the option will be in-the-money. By rounding up to the nearest integer “a” the value of for n = 1, 2, 3, and 4 (see rows 11 and 12 below), we determine that the 1 timestep call will only be in the money at the u node, the 2 timestep call will only be in the money at the uu node, the 3 timestep call will only be in the money at the uuu and uud nodes, and the 4 timestep call will only be in the money at the uuuu and uuud nodes. This greatly simplifies the calculations for call prices because we know that the call payoffs will all be zero at all other nodes (see row 13 below). Having determined the arbitrage-free call prices, then we find the arbitrage-free put prices by applying the put call parity equation (you can bring up the spreadsheet by clicking on the screenshot below):