A two-month European put option on a dividend-paying stock is currently selling for $2. The stock will pay a $1 dividend in one month. The current stock price is $48, the puts strike price is $50, and the risk-free interest rate is 6% (annualized, simply compounding). (a) By using the lower bound of an European put option, what opportunities are there for an arbitrageur? (b) Would the above market prices still provide an arbitrage opportunity if the stock will not pay a dividend within the next two months while the stock remains the same? (c) Under the situation in (a), what is the price of an European call option having the same strike price and maturity?