2/16/12
Problem Set 4
Futures Options
Problem 1
•  If underlying futures contract expires at day 90, then this is not an
equilibrium situation
•  Sell a call and buy a put, receiving $2.25
Ø  Now obligated to sell a futures contract with futures price of $100
•  Purchase listed futures contract with futures price $102 (at no
immediate cost)
•  So, you have $2.25 today with the obligation to pay $2 on day 90
•  Equilibrium would occur if you received $2.25 immediately with
obligation to pay $2.31 on day 90 (borrow at 10%)
Ø  So if futures price were 102.31, would be balanced
1
2/16/12
Problem 2
•  Actual premium paid for the contract is 500* $4.875 =
$2,437.50
Ø This is the maximum potential loss
Ø Maximum loss would occur if price at expiration were
at or below the strike price (485 or less)
Ø Breakeven futures price is 485 + 4.875 = 489.875
•  If price at expiration were 490, profit would be 500*0.125
= $62.50
•  If price at expiration were 495, profit would be 500*5.125
= $2562.50
Problem 3
•  Actual premium paid for the contract is 500* $6.75 = $3,375
Ø  This is the maximum potential loss
Ø  Maximum loss would occur if price at expiration were at or above
the strike price (485 or higher)
Ø  If price at expiration were 480, loss would be 500*1.25=$875
Ø  Breakeven futures price is 485 – 6.75 = 478.25
•  If price at expiration were 475, profit would be 500*3.25 = $1625
•  If price at expiration were 470, profit would be 500*8.25 = $4125
2
2/16/12
Problem 4: covered call
•  Buy underlying futures contract and write a call
Ø  Underlying costs nothing at origination date
Ø  Sale of call would provide income of 500*4.875=$2437.50
•  If price at expiration were 485 or less, option would expire worthless
and the futures position would dominate
Ø  At 470, loss would be 2437.50-500(483.10-470)= –4112.50
Ø  At 475, loss would be 2437.50-500(483.10-475)= –1612.50
Ø  Breakeven futures price is 483.10 – 4.875=478.225
Ø  2437.50-500(483.10- 478.2255)= 0
Ø  At 480, profit would be 2437.50-500(483.10-480)= 887.50
Ø  At 485, profit would be 2437.50-500(483.10-485)= 3387.50
Ø  This is the maximum profit, because option would be exercised if
futures price above 485
Problem 5: protective put
•  Buy underlying futures contract and buy a put
Ø  Underlying costs nothing at origination date
Ø  Purchase of put would cost 500*6.75=$3375
•  If price at expiration were 485 or higher, put would expire worthless
and the futures position would dominate
Ø  At 495, profit would be 500(495–483.10)–3375 = 2575
Ø  At 490, profit would be 500(490–483.10)–3375 = 75
Ø  Breakeven futures price is 483.10 + 6.75=489.85
Ø  500(489.85–483.10) - 3375= 0
Ø  At 485, loss would be 500(485–483.10)–3375 = –2425
Ø  This is the maximum loss, because option would be exercised if
futures price below 485
3