Question $4$

$4.$ United Airlines $($UA$),$ a U$.$S$.$ company, bought an aircraft, A$380,$ from Airbus, a European company. And the payment of E$50$ million is due in three months. UA is concerned with the dollar costs of international purchase and would like to control exchange risk. The current spot exchange rate is $\frac{0\mathrm{.}95}{\text{\$}}$ and $3-$month forward exchange rate is $\frac{0\mathrm{.}96}{\text{\$}}$ at the moment. The premium of a $3-$month put option on euros with a strike price of $$\frac{1\mathrm{.}04}{}$ is $$0\mathrm{.}01$ per euro, and the premium of a $3-$month call option on euros with a strike price of $$1\mathrm{.}04/$euro is $$0\mathrm{.}02$ per euro. Currently, three$-$month interest rate is $1\mathrm{.}5\%$ in the euro zone and $1\mathrm{.}0\%$ in the U$.$S$.$

$($a$)$ How should UA hedge exchange risk using forward contract? What is the future dollar cost of meeting this obligation using the forward hedge?

$($b$)$ How should UA hedge using options? What would be the 'expected' dollar cost of meeting this obligation with option hedging? Assume that UA regards the current forward exchange rate as an unbiased predictor of the future spot exchange rate.

$($c$)$ What are the maximum and minimum dollar costs of meeting the obligation if UA using option hedging? Explain.

$($d$)$ At what future spot exchange rate do you think UA will be indifferent between the option and forward hedges? What is the range of future spot rate UA prefers option hedge over forward hedge?