1.The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%.

A.What is the price of a European put option that expires in six months and has a strike price of $30? (20 points)

B.Explain carefully the arbitrage opportunities if the European put price is $2. (30 points)

2.In what conditions, early exercise of American put is more attractive? (10 pts)

3.Suppose you buy a call and put option that has the same strike price of $75 and same maturity. Call costs $5 and put costs $4. Graph the profits and losses at expiration for different stock prices? (You need to draw call and put in the same graph) If the stock price at maturity is $80, what is your profit or loss? (40 pts)