Using options to build hedge portfolio. Consider a put option on the British pound $($BP$)$ which represents the right to sell $1,000$ at the strike price of $$1\mathrm{.}50$ per $.$ The option will expire in one year. The current spot rate is $$1\mathrm{.}32$ per f$.$ In the future, the spot rate may become $$1\mathrm{.}40$ or $$1\mathrm{.}50$ per f$.$ The annual risk$-$free interest rate is $6\mathrm{.}0\%$ 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 $952\mathrm{.}38$ now. $($a$)$ If you buy a British bond, how many puts 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 put option?