Problem
Consider a call option on the British pound (BP) which represents the right to purchase £1,000 at the strike price of $1.45 per £. The option will expire in one year. The current spot rate is $1.45 per £ (at the strike). In the future, the spot rate may become $1.40 or $1.50 per £. The annual risk-free interest rate is 2.0% in the US and 2.5% in the UK. A pure-discount British bond, that will pay £1,000 on the maturity date, is selling for £968.15 now.
i. 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?
ii. What is the fair price of this call option?
iii. 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.