Question

A bank’s position in options on the dollar-euro exchange rate has a delta of 30,000 and a gamma of -80,000.

a) Explain how these numbers can be interpreted. The exchange rate is 0.9 Eur / USD.
b) What position would you take to make the position delta neutral?
c) After a short period of time, the exchange rate moves to 0.93 Eur / USD. Estimate the new delta.
d) What additional trade is necessary to keep the position delta neutral?
e) Assuming the bank did set-up a delta neutral position originally, has it gained or lost money from the exchange-rate movement?

Answer 1

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Answer:

a)

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 01*30000 = 300. The gamma indicates that when the euro exchange rate increases by $0.01. the delta of the portfolio decreases by 0 01*80000 = 800

b)

For delta neutrality 30,000 euros should be shorted

c)

When the exchange rate moves up to 0.93, we expect the delta of the portfolio to decrease by (0 930-90)*80 000 =2400 so that it becomes 27,600

d)

Additionally to maintain delta neutrality, it is therefore necessary for the bank to unwind its short position 2,400 euros so that a net 27,600 have been shorted

e)

When a portfolio is delta neutral and has a negative gamma, a loss is experienced when there is a large movement in the underlying asset price. We can conclude that the bank is likely to have lost money.