Over the next five months, the stock price of Aspirant Enterprises Ltd. is expected to have monthly volatility 0.1. The stock price today is $11 per share. The risk-free interest rate is currently 2% per annum (continuous compounding); this is not expected to change over the five-month time horizon. (a) Create a binomial model of the stock price over the next five months, with monthly time steps. Give the parameters of the model (you need not sketch the whole tree). (b) Find the value of a European put option on Aspirant stock with a strike price of $10 and expiry in five months' time. (c) Find the value of a European call option on Aspirant stock with a strike price of $10 and expiry in five months' time. (d) Verify that the European call and European put prices satisfy put-call parity. (e) If the put option were American, would it ever be optimal to exercise it early at any of the nodes of the tree?