A non-dividend-paying stock selling at $100 will either go up at the rate of u = 1.1 or go down at the rate of d = 0.9 each month for the next 2 months. The annual interest rate is 5% with monthly compounding.

a) Construct a two-period binomial tree to calculate the price of a European call option expiring in two months with strike X = $95.

b) There is another European put option on the same underlying stock with a strike $95. The put option will also expire in two month. The put is priced at $2.5. Is there any arbitrate opportunity? If yes please show clearly how you can arbitrage. If not, please explain why.