A stock price is currently trading at $50. Over each of the next two 3-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. Please Show Your Work. a. What is the value of a 6-month European call option with a strike price of $51?

b. What is the value of a 6-month European put option with a strike price of $51? c. Using your answers from parts a. and b. to verify if the put-call parity holds. d. If the put option is American, would it ever be optimal to exercise it early at any of the nodes on the tree?