Question

Alfred owes GBP 1M in one year, but all of his assets are in USD. He...

Alfred owes GBP 1M in one year, but all of his assets are in USD. He wishes to use options to reduce his exposure to exchange rates. He has the following options available to him for purchase. You may ignore option premia for the purposes of this question, and assume he can choose an option with whatever quantity of the underlying asset he wishes – if he chooses an option with USD as the underlying, he can choose any quantity of USD.

Option Strike Maturity Underlying Asset
Long Call USD 1.25 per GBP 1 Year GBP
Long Put USD 1.15 per GBP 1 Year USD
Long Put USD 1.20 per GBP 1 Year GBP
Long Call USD 1.10 per GBP 1 Year USD

4A. Which one of these options should he choose?

4B. What should he set the underlying asset to?

4C. Will he exercise the option if the spot rate is USD 1.19 per GBP in one year?

4D. If the spot rate is USD 1.19 per GBP in one year, what exchange rate will he actually be buying his GBP at?

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Answer #1

Liability = GBP 1M

If the dollar depreciates with respect to GBP, say from $1.1/GBP to $1.3/GBP (hypothetical figures), then Alfred will have to pay more in dollars for the same GBP 1M i.e loss to Alfred.

Therefore Alfred should go long on put options with USD as underlying asset that will allow him to sell USD at an appreciated rate with respect to GBP

4A)

Long Put USD 1.15 per GBP 1 Year USD


4B) USD

4C) K : strike price = USD1.15/GBP

S: spot rate = USD1.19/GBP

Since S<K, the put option will be exercised

4D) Since the put option has been exercised, he will buy GBP at an exchange rate of USD1.15/GBP

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