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Solutions and discussion for questions related to option pricing, focusing on intrinsic value, time value, and the comparison between september and march options. It also covers the calculation of dividends from spot-futures parity and the comparison of payoffs between a long call and a short put strategy.
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MSc 2010 Tutorial 4 Solution guidelines
Q This is about intrinsic value and time value.
March 1800 call is ‘deep in-the-money’, ie a large amount of intrinsic value (226). There is only a small amount of time value (6), principally because of the short time to expiration. The March 1800 put has zero intrinsic value and there is very little chance of moving into the money in the next 42 days (S needs to fall below 1800). Hence time value is only 3.
September options are worth more than March options with the same K because of time value. Time to expiration is much longer (224 days) so there is more opportunity for a large price change.
First find the value of the dividend from spot-futures parity. I = S 0 F 0 e rT = 2026 2014.1e 0.008 224/365) = 21.
Cost of PP = 2026 + 124.5 = 2150. Cost of SH = 2026 + zero cost of futures contract i. S (^) T = 1800
PP: exercise @ 2000 outcome 2000 2150.5 = 150.
SF: Convergence F (^) T = S (^) T = 1800 Gain on futures 2014.1 1800 = 214. Loss on share = 226 FV of Div = 21. Net result = +9. ii. S (^) T = 2200
PP: do not exercise outcome 2200 2150.5 = 49.
SF: Convergence F (^) T = S (^) T = 2200 losson futures 2014.1 22 00 = 185. gain on share = 174 FV of Div = 21. Net result = +9. ****Discuss the different outcomes**
(a) Cost of March 1800 and 2200 calls 232 + 4 = 236 Write two March 2000 calls 2 × 65.5 = + Total = 105
Cost of the strategy is 105p
The payoffs from the calls are the intrinsic values at expiration. Calls are exercised against the writers, hence intrinsic values are negative payoffs for written calls.
Payoffs from calls at various expiration date share prices (S (^) T )
S (^) T 1700 1800 1900 2000 2100 2200 2400 1 long 1800 0 0 100 200 300 400 600 2 short 2000 0 0 0 0 200 − 400 − 800 1 long 2200 0 0 0 0 0 0 200 Total payoff 0 0 100 200 100 0 0 Cost of strategy − 105 − 105 − 105 − 105 − 105 − 105 − 105 PROFIT − 105 − 105 5 95 5 − 2 − 2
Profit if the market is relatively stable around a price of 2000. Discuss, and perhaps compare with a short straddle.
NB, break even points: profit = 0, when ST = 1905 and 2095. Hence the strategy profits if ST is within that range. Maximum gain if S (^) T = middle of the 3 exercise prices, ie 2000 in this example
Butterfly spread 95180022002000 S (^105) T