You know all about plain vanilla currency options but X Corp hired you evaluate a digital currency option on British Pounds(BP) that pays 1 BP if the British currency appreciates relative to the dollar and zero if it depreciates. The current $/BP exchange rate is 1 and you expect it to be either 2 or 0.50 in a year. A one-year US Treasury zero coupon bond with a face value of $100 is trading at $80 today while a one-year UK government bond with par value of 100BP is trading at 90.90BP today.

1. Can you create a replicating (the digital option) portfolio involving the foreign and home currency risk-free bonds?

2. Can you then price the digital option?

3. What would be the price of a digital option that paid 1BP when the currency depreciates and 0 when it appreciates?

PS: feel free to use any assumptions, but need to be clear of them