One year ago, you sold a put option on 100,000 euros with an expiration date of
ID: 2772909 • Letter: O
Question
One year ago, you sold a put option on 100,000 euros with an expiration date of one year. You received a premium on the put option of $.04 per unit. The exercise price was $1.22. Assume that one year ago, the spot rate of the euro was $1.20, the one-year forward rate exhibited a discount of 2%, and the one-year futures price was the same as the one-year forward rate. From one year ago to today, the euro depreciated against the dollar by 4 percent. Today the put option will be exercised (if it is feasible for the buyer to do so).
Determine the total dollar amount of your profit or loss from your position in the put option.
Now assume that instead of taking a position in the put option one year ago, you sold a futures
contract on 100,000 euros with a settlement date of one year. Determine the total dollar amount of your profit or loss.
Explanation / Answer
Put option
Exercise price =1.22
Spot price = 1.20
Premium = 0.04
Since, spot price is lower than exercise price, put the put buyer will exercise this option.
Profit per unit of put = premium – (Strike price – spot price
= 0.04 – (1.22-1.20)
= 0.02
Total no. of units= 100,000
Total profit = 0.02 x 100,000
= $2,000
Futures
Futures price = current spot rate x( 1+ discount rate)^t
= 1.20 x ( 1+0.02)^1
= 1.224
After one year, spot rate is 1.20. Therefore profit per unit of future will be
Profit per unit of future = 1.224 – 1.20
= 0.024
Total profit = 0.024 x 100,000
= 2400
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