Mr. Ramzan is a fund manager and invests mostly in stocks. He has been interested in a stock whise current price is $33. He also knows that the price can either go up to $37 and go down to $30 at the end of 3 months. The risk free rate is 8 percent.

(a) Calculate the value of a three month American as well as Europeon call option on the stock with an ecercise price of $31.

(b) Can the possibility of, "No arbitrage" exist in either of the two cases? If yes, why? And if not, why not? Support your answer by explaining how the arbitrage could be built.

(c) What would happen if both the options are put options i.e. American put and Europeon put. Would the answer to part b change? If so why?

(d) If Mr. Ramzan is of the view that put-call parity always holds, how would have he developed the portfoio. Do you think that it is possible under the given circumstances the parity would hold? Explain in complete detail by taking the data considerations where necessary.