ASM Practice Exam 8: Q3

[aisha]

Could someone explain how to understand this question and do it in a simple way. I'm finding it hard to understand what the answer says.
Thanks

[arbiter]

spot exchange rate = $2/pound or (0.5pound/dollar-we'll be needing this later)

r(dollar) = 0.04= d (pound denominated)
r(pounds) = .06 = r

##-----------Get --------------- Give ------------- price
Have-------100 dollars-----------40 pounds--------10.50 pounds
want----------100 pounds------- 250 dollars-------- x

Since the first option is a pound denominated option, it is a call option with 40 pounds as strike (since we give pounds) and 100 dollars as stock (since we get this). So, this will be a 100 (number of "stock") pound-denominated call option with spot exchange rate = 0.5pounds/dollar (given) and strike rate = 40pounds/100dollars, r= 0.06 and d = .04 and call price of one option = .1050 pounds.

By put call parity, the value of one put with the same time to expiry and the same strike price is = 0.004020 pounds

But what we want to find is the price of an option to purchase 100 pounds with 250 dollars. Using a pound-denominated option, this is a put option (since pounds is strike --that's what we're going to get by giving up dollars, and dollars as stock). So, we need a price for 250 such put options.

therefore, the total value of 250 put options = 250*0.004020=1.004965 pounds.

But since the question asks for the value in dollars, convert the pounds into dollars using the spot exchange rate. Hence, the option price = 1.004965*2=2.0099~2.01dollars.
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Hope this helps.