# If you buy a British bond, how many calls do you have to buy or sell to construct a risk-free hedge portfolio? What is the future dollar value of the hedge portfolio?

1. Consider a call option on the British pound (BP) which represents the right to purchase £1,000 at the strike price of \$1.30 per £. The option will expire in one year. The current spot rate is \$1.32 per £. In the future, the spot rate may become \$1.40 or \$1.50 per £. The annual risk-free interest rate is 6.0% in the US and 5% in the UK. A pure-discount British bond, that will pay £1,000 on the maturity date, is selling for £952.38 now.

(a) If you buy a British bond, how many calls do you have to buy or sell to construct a risk-free hedge portfolio? What is the future dollar value of the hedge portfolio? (b) What is the fair price of this call option? (c) Suppose the call is trading for \$20 per contract. Show how you can realize arbitrage profit and determine the profit. Assume you buy or sell one unit of British bond.