20. The stock price of Microsoft (MSFT) on December 22 is $25.50. The traded option prices for calls and puts maturing on January 21, and February 18 (i.e., in one and two months) are as follows:
| Maturity (T) | Strike (K) | Calls | Puts |
| January 21 | 27 | 1.65 | 3.15 |
| February 18 | 25 | 2.45 | 1.80 |
| 27.5 | 1.51 | 3.36 | |
| 30 | 0.83 | NA |
Assume the interest rate is zero.
Use this information to build a two-period implied binomial tree that fits this set of options as best as possible. Each period will be for one calendar month.
Your tree will have an initial stock price node and two periods thereafter. Since the tree is recombining, you will have altogether 6 nodes on your tree. At each node, show the stock price, and the branching probability. State any assumptions you make clearly.
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