Michael has ordered a Rolls Royce car for 200,000 British pounds, which he will pay when the car is delivered to him in three months. Because Michael has got an A+ in ACTS:4830 from the devilish instructor, Apple Lo, as a reward his insanely rich mum has promised to give him US $320,000 three months from now.

Worried about the US dollar losing value relative to the British pound, Michael now decides to buy appropriate 3-month at-the-money European currency gap options to exactly cover the shortfall in case it occurs. To lower his cost, Michael is willing to take a smaller payoff (than the payoff before buying any gap options) if the 3-month dollar/pound exchange rate is between 1.50 and 1.60.

You are given:

(i) The current dollar/pound exchange rate is 1.60.

(ii) The continuously compounded risk-free interest rate in the United States is 1%.

(iii) The continuously compounded risk-free interest rate in the United Kingdom is 2%.

(iv) The volatility of the exchange rate of dollar per pound is 20%.

Describe the gap options that Michael should buy. Hence calculate the total cost of the currency gap options in US dollars.