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I am trying to properly calculate the delta, vega and theta for an options strategy that involves buying a 90 day ATM SPX put and selling a 90 day ATM VIX call.

Here is what I have done so far:

  • SPX = 5600
  • VIX = 16
  • SPX put Delta = -0.5
  • VIX call Delta = 0.5
  • VIX/SPX Beta = -5.42
  • SPX put Vega = 11.9
  • VIX call Vega = 0.038
  • SPX put Theta = -1.17
  • VIX call Theta = -0.012
  • The Beta is from 1 year historical daily return data.
  • Combined Delta = (-0.5) - (-5.42 x 0.5) = 2.21
  • Combined Vega to SPX = (11.9) - (0.5) = 11.4
  • Combined Theta = (-1.17) - (-0.012) = -1.16

Perhaps this is correct but I am doubtful because its long the SPX but somehow also long volatility which makes no sense.

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  • $\begingroup$ Long options in general tend to be long volatility, there is no contradiction. $\endgroup$
    – KaiSqDist
    Commented Aug 2 at 0:45
  • 2
    $\begingroup$ VIX call vega is SPX volga. VIX call delta is SPX vega. $\endgroup$
    – Frido
    Commented Aug 2 at 15:01

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