Consider a call option on the British pound which represents the right to purchase 1,000 at the

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Question:

Consider a call option on the British pound which represents the right to purchase £1,000 at the strike price of $1.50 per £. The option will expire in one year. The current spot rate is $1.47 per £. In the future, the spot rate may become $1.40 or $1.60 per £. The annual risk-free interest rate is 2.0% in the US and 3% in the UK. A pure-discount British bond, that will pay £1,000 on the maturity date, is selling for £958 now.

(1) 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?

(2) What is the fair price of this call option?

(3) 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.