DES shares are currently trading at $38 per share. The stock pays no dividends. A one-year European put option on DES with an exercise price of $40 is currently trading at $3.10.

1. If the risk-free interest rate is 5% per year, what is the price of a one-year European option to buy DES with an exercise price of $40?

2. Is there an arbitration opportunity: a. If the option to purchase on DES is trading at $2.50? If so, what do you need to do to exploit this arbitration opportunity?

b. If the option to purchase DES is trading at $3? If so, what do you need to do to exploit this arbitration opportunity?

c. If the option to purchase des DES is trading at $3.50? If so, what do you need to do to exploit this arbitration opportunity?