A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. (a) What is the value of a six-month European call option with a strike price of $51? (b) What is the value of a six-month European put option with a strike price of $51? (c) Verify that the European call and European put prices satisfy put-call parity. (d) If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree?