You observe the following quotations of currency options on Euro. They are European put options

expiring in six months. Contract size is $10,000.$

Strike rate Premium $($per $)$

Put Option #$1$ US$$1\mathrm{.}06/$ US$$0\mathrm{.}042$

Put Option #$2$ US$$1\mathrm{.}04/$ US$$0\mathrm{.}033$

$($a$)$ Suppose you would like to buy one contract of one of these options to speculate on the depreciation

of $$ over the next six months. Plot and compare the net profit$/$loss profiles $($in US$$)$ of the buyers of

the two put options as a function of the spot exchange rate to be realized in six months. What are the

respective break$-$even exchange rates of the two options? What is the range of the realized spot

exchange rates that will result in the outcome $($based on net profit$/$loss$)$ from using Option #$1$ being

worse than that of Option #$2?$ Comment on the differences in using the two options to speculate on $$

depreciation.

$($b$)$ Suppose you operate a US firm selling electronic components to customers in Germany. Your firm

will be receiving $10,000$ from a customer in six months. You would like to hedge against the

depreciation of $$ by buying one of the above two put options. Plot and compare the net hedged US$

cash flows by using Option #$1$ vs$.$ Option #$2$ as a function of the spot exchange rate to be realized in

six months $($make sure to account for the option prices paid upfront in arriving at the net cash flows$).$

What are the minimum net hedged US$ cash flows respectively by using Option #$1$ and Option #$2$ to

hedge? Comment on the differences in using the two options to hedge against the FX risk of your $$

receivable.