To settle an urgent debt payable in US dollars in one year, Jeff has decided to (reluctantly!) sell his favorite Rolls Royce car in exchange for a fixed sum payable in British pounds in one year. Because the British pound may lose value relative to the US dollar, Jeff decides to buy appropriate 1-year dollar-denominated $1.6-strike currency options on pounds to hedge against the exchange rate risk, but he is not sure about whether he should buy European or American options.

You are given:

(i) The continuously compounded risk-free interest rate on dollars is 6%.

(ii) The continuously compounded risk-free interest rate on pounds is 8%.

Sketch two separate graphs to show the possible (dollar) prices of each European and American currency option that Jeff should buy against the current dollar/pound exchange rate, X(0). Shade the relevant regions and clearly indicate the equations of the relevant boundaries.