(a) A stock price is currently $50. It is known that at the end of six months it will be either $55 or $45. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a six-month European put option with a strike price of $48? (b) What is the corresponding call price of the stock given in part (a)? (c) Verify that the put price and the call price calculated in parts (a) and (b) satisfy the put-call parity. (d) Does the put option price calculated in part (a) satisfy the lower bound principle?