Consider a UK.-based IMporter of bicycles, Italian bicycles, who has a €160,000 payable due in one year. He wants to use options to hedge the cost of his payable. One-year at-the-money put and call options on €10,000 exist. The spot exchange rates are €1.00 = $1.120 and £1.00 = $1.400, which makes the spot cross rate €1.00 = £0.80. In the next period, the euro can increase in pound value to £1.00/€1.00 or fall to £0.64/€1.00. The interest rate in dollars is i$ = 0%; the interest rate in euro is i€ = 5.00%; the interest rate in pounds is i£ = 7.10%.
- How many at-the-money puts (on €10,000 strike price in £8,000) should he sell today? HINT: You should be able to verify that your hedge “works” if the exchange rate at time 1 is £1.00/€ or £0.64/€ i.e. you should have the same cash flow in either state.