A cylinder option on the sale of foreign currency is a contract defined as follows:
If S T > X1, you sell foreign exchange at X1, the floor
• If S T > X2, where X2 > X1, you sell at X2, the cap
• If X1 ≤S T ≤ X2, you sell at S T.
• Thiscontractrestrictstheuncertaintyaboutthefuturessalespricetotherange
X1 ≤S T ≤ X2.
For instance, Barrel Imports has a sales contract to sell cad against usd:
• At X1 = usd/cad 0.80 if the cad trades below 0.80.
• At X2 = usd/cad 0.90 if the cad trades above 0.90.
• The spot rate if that rate is between 0.80 and 0.90.
(a) Show the payoff of the contract graphically.
(b) Show that it can be viewed as a combination of European-style options.
(c) Illustrate the value of a foreign currency claim hedged with such a contract.