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 |
| 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 |
| 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!