4) An American firm will receive 10,000,000 in about five months. Todays spot exchange rate is 1.2650 $/. The firm decides to hedge this cash inflow using options. The US $ interest rate is 2.75% and the interest rate is 1.25%. The firm contacts their bank which offers the following options on the :

• American call option on the with T = 3 months, K = 1.2600 US$/, and a price C=0.0055 US$/
• American put option on the with T = 3 months, K = 1.2600 US$/, and a price P=0.0025 US$/
• American call option on the with T = 6 months, K = 1.2600 US$/, and a price C=0.0075 US$/
• American put option on the with T = 6 months, K = 1.2600 US$/, and a price P=0.0035 US$/
• American call option on the with T = 9 months, K = 1.2600 US$/, and a price C=0.0095 US$/
• American put option on the with T = 9 months, K = 1.2600 US$/, and a price P=0.0045 US$/

Answer the following questions, assuming that these options have no resale value, and ignoring transactions costs.

a) Which option should the firm choose and why?

b) What is the minimum value in US$/ that the firm can establish in this hedge?

c) Suppose that five months later (i.e., at the time when firm receives 10,000,000) the spot exchange rate is 1.2475 US$/. What should firm do? How many US$ will the firm receive for the 10,000,000 after considering the initial cost of buying the option?

d) Now suppose that at the time (five months later) the firm receives 10,000,000 the spot exchange rate is 1.2825 US$/. What should the firm do? How many US$ will the firm receive for 10,000,000, after considering the initial cost of buying the option?