How Option Greeks Change as Futures Move Between Strikes
Summary
The example considers a position short August puts, long August calls at a higher strike, and short futures. Its initial net delta, gamma, and vega are reported as slightly negative or close to zero. The question asks why the answer key says all three become positive when futures rise, with other conditions unchanged.
The reply explains the change in terms of distance from the strikes: as futures move away from the short put strike and nearer the long call strike, the calls become closer to at-the-money. At-the-money options tend to have more gamma than options farther in or out of the money, so the long calls' positive gamma and vega can outweigh the short puts' contributions. Delta also shifts as the underlying rises. The initial Greeks describe local sensitivities; they do not remain fixed across underlying prices. The answer is qualitative and does not recalculate the position's Greeks along the move.
Key ideas
- A portfolio's initial net Greeks are local sensitivities and can change as futures prices move.
- Moving away from the short put strike and closer to the long call strike can increase the calls' influence.
- Options nearer at-the-money generally have more gamma than options farther in or out of the money.
- The reply attributes the changing delta, gamma, and vega to the position's shifting relation to its strikes.
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Full text
# Change in price of underlying impact on delta gamma and vega # Change in price of underlying impact on delta gamma and vega I am working my way through Natenberg's book as well as the accompanying workbook, and there is a question I cannot figure out (p86). - Futures price = 149.65 - time to August expiration = 8 weeks - annual volatility = 24.20% You have the following position: - -32 August 140 puts - +30 August 160 calls - -15 August futures contracts with the options having these risk sensitivities | option | delta | gamma | theta | vega | | Aug 140 put | -22.6 | 2.12 | -.0381 | .176 | | Aug 160 call | 25.5 | 2.26 | -.0407 | .188 | I correctly calculated that the greeks for my position were | delta | gamma | theta | vega | | -11.8 | -0.04 | +0.0018 | 0.008 | The question is What will happen to your delta, gamma, and vega position if the futures price rises while all other market conditions remain unchanged? The answers say that the delta, gamma, and vega would all become positive. I don't see how, with rising prices and negative gamma, even if its very small, the delta becomes positive. Why does the gamma and the vega become positive as well? Would somebody please explain to me why this is the case? Thank you in advance! ## Answer by user68819 (score 0) https://quant.stackexchange.com/a/79665 Without having done the maths myself - as you drift away from the short put strike towards the long call strike, your gamma also starts becoming more positive. This is because the future drifts away from the short put strike of 140 to being closer to the 160 long calls (atmf options habe more gamma than otm/itm options). This also naturally means that you start accruing deltas, as you drift. The small -ve gamma that you calculate is only locally correct, gamma also changes with the level of the underlying with respect to the strikes of the portfolio. The vega becoming (more) positive has a similar rationale.
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