BUS325 Derivative Securities
Workshop 12
Problem 17.11.
What is the delta of a short position in 1,000 European call options on silver futures? The options
mature in eight months, and the futures contract underlying the option matures in nine months. The
current nine-month futures price is $8 per ounce, the exercise price of the options is $8, the risk-free
interest rate is 12% per annum, and the volatility of silver is 18% per annum.
The delta of a European futures call option is usually defined as the rate of
change of the option price with respect to the futures price (not the spot price).
In this case F0 8 , K 8 , r 012 , 018 , T 06667
(N.B. T is expiry of option – not the futures.)
the delta of the option is
The delta of a short position in 1,000 futures (call) options is
therefore: -1000 x 0.4886 = 4886 .
1
, 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?
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
The gamma indicates that when the euro exchange rate increases by
$0.01 the delta of the portfolio decreases by
2
Workshop 12
Problem 17.11.
What is the delta of a short position in 1,000 European call options on silver futures? The options
mature in eight months, and the futures contract underlying the option matures in nine months. The
current nine-month futures price is $8 per ounce, the exercise price of the options is $8, the risk-free
interest rate is 12% per annum, and the volatility of silver is 18% per annum.
The delta of a European futures call option is usually defined as the rate of
change of the option price with respect to the futures price (not the spot price).
In this case F0 8 , K 8 , r 012 , 018 , T 06667
(N.B. T is expiry of option – not the futures.)
the delta of the option is
The delta of a short position in 1,000 futures (call) options is
therefore: -1000 x 0.4886 = 4886 .
1
, 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?
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
The gamma indicates that when the euro exchange rate increases by
$0.01 the delta of the portfolio decreases by
2
