A bank’s position in options on the dollar–euro exchange rate has a delta
Problem 17.22.
A bank’s position in options on the dollar–euro exchange rate has a delta of 30,000 and a gamma of -80,000. Explain how these numbers can be interpreted. The exchange rate (dollars per euro) is 0.90. What position would you take to make the position delta neutral? After a short period of time, the exchange rate moves to 0.93. Estimate the new delta. What additional trade is necessary to keep the position delta neutral? Assuming the bank did set up a delta-neutral position originally, has it gained or lost money from the exchange-rate movement?
Hint
The delta indicates that when the value of the euro exchange rate increases by $0.01, the value of the bank’s position increases by 0.01X30,000 - $300 . The gamma indicates that when the euro exchange rate increases by $0.01 the delta of the portfolio decreases by 0.01X80,000 = 800 . For delta neutrality 30,000 euros should be shorted. When the exchange rate moves up to 0.93, we expect the delta o...
The delta indicates that when the value of the euro exchange rate increases by $0.01, the value of the bank’s position increases by 0.01X30,000 - $300 . The gamma indicates that when the euro exchange rate increases by $0.01 the delta of the portfolio decreases by 0.01X80,000 = 800 . For delta neutrality 30,000 euros should be shorted. When the exchange rate moves up to 0.93, we expect the delta of the portfolio to decrease by (0.93-0.90)X80,000=2,400 so that it becomes 27,600.
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