Consider a European call option and a European put option, both with strike price 13. The two options are on the same underlying stock that currently trades for 12 and may at either 14 or 9 in one year. The risk-free rate is 3% (annually compounded). The expiration. Date when the options can be exercised is in one year.

1. Draw a binomial tree and calculate the price of the European call using the risk neutral probability method.
2. Draw a binomial tree and calculate the price of the European put using the risk neutral probability method.
3. Verify that the put call parity formula holds. To do so, recompute the price of the European put option from part (b) by using the put-call parity formula and the result for the call price you obtained in (a). Assume that the company is known to pay no dividends.