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## Q. 8.MSE.7

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 \$.05 per unit. The exercise price was \$1.22. Assume that one year ago, the spot rate of the euro was \$1.20. One year ago, the one-year forward rate of the euro exhibited a discount of 2 percent, and the one-year futures price of the euro was the same as the one-year forward rate of the euro. 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).
a. Determine the total dollar amount of your profit or loss from your position in the put option.
b. One year ago, Rita sold a futures contract on 100,000 euros with a settlement date of one year. Determine the total dollar amount of her profit or loss.

## Verified Solution

a. The spot rate depreciated from \$1.20 to \$1.152. You receive \$.05 per unit. The buyer of the put option exercises the option, and you buy the euros for \$1.22 and sell them in the spot market for \$1.152. Your gain on the put option per unit is (\$1.152 – \$1.22) + \$.05 = -\$.018 Total gain = -\$.018 × 100,000 = -\$1,800
b. The futures rate one year ago was equal to: \$1.20 × (1 – .02) = \$1.176. So the futures rate is \$1.176. The gain per unit is \$1.176 – \$1.152 = \$.024 and the total gain is \$.024 × 100,000 = \$2,400