Question B. A Short-Answer Question. (10 marks in Total)

The price of a stock, which pays no dividends, is $24 now and the strike price of a one-year European put option on the stock is $25. The risk-free rate is 3% (continuously compounded).

(a) An investor buys two one-year European puts today. At the maturity day, if the stock price is 22 dollars, will the investor exercise this put option? What is the gross payoff for this investor? (2 marks)

(b) Suppose that the price of this put is 3 dollars. Under the no-arbitrage condition, what is the price of a one-year European call option with a strike price of $25? (2 marks)

(c) Suppose that both this European call and European put with a strike price of 25 are sold for 2 dollars. Are there any arbitrage opportunities here? If yes, identify the arbitrage opportunity and calculate the arbitrage profit. If no, provide your calculations to support your conclusions. (4 marks)

(d) Why the early exercise of an American put is more attractive if the risk-free rate increases and volatility decreases? (2 marks)