The DoubleStep stock price is currently $79 per share. Over each of the next two six-month periods it is expected to go up by 5% or down by 6%. All the options mentioned below are on this stock. The continuously-compounding risk-free interest rate is 4% per annum.

(a) What is the value of a one-year European call option that strikes at $80?

(b) What is the value of a one-year European put option that strikes at $80?

(c) Do the European call and put option values satisfy the put-call parity? Show your verification.

(d) If the put option were American, would it ever be optimal to exercise before maturity? What would be the value of the option?