P$5$: Assume that today is March $7,$ and, as the newest hire for Goldman Sachs, you must advise a client on the costs and benefits of hedging a transaction with options. Your client $($a small US exporting firm$)$ is scheduled to receive a payment of $6,250,000$ on April $20,44$ days in the future. Assume that your client can borrow and lend at a $6\%$ p$.$a$.$ US interest rate.

$1.$ Describe the nature of your client's transaction exchange risk.

$2.$ What is the minimum dollar revenue your client will receive in April? Remember to take account of the opportunity cost of doing the option hedge.

$3.$ Determine the value of the spot rate $($$$/)$ in April that would make your client indifferent ex post to having done the option transaction or a forward hedge.

The forward rate for delivery on April $20$ is $$1\mathrm{.}30/.$

$4.$ Use the appropriate American option with an April maturity and a strike price of $129$c$/$ to determine the dollar cost today of hedging the transaction with an option strategy. The cost of the call option is $3\mathrm{.}93$c$/,$ and the cost of the put option is $1\mathrm{.}58/.$

P$6$: Assume that today is September $12.$ You have been asked to help a British client who is scheduled to pay $1,500,000$ on December $12,91$ days in the future.

Assume that your client can borrow and lend pounds at $5\%$ p$.$a$.$

$1.$ Describe the nature of your client's transaction exchange risk.

$2.$ What is the option cost for a December maturity and a strike price of $0\mathrm{.}72/$ to hedge the transaction? The option premiums per $100$ euros are $1\mathrm{.}70$ for calls and $2\mathrm{.}40$ for puts.

$3.$ What is the minimum pound cost your client will experience in December?

$4.$ Determine the value of the spot rate $(/)$ in December that makes your client indifferent ex post to having done the option transaction or a forward hedge if the forward rate for delivery on December $11$ is $0\mathrm{.}70/.$