Combining SPX and VIX Option Greeks Across Underlyings

Summary

The document examines how to combine the delta, vega, and theta of a long at-the-money SPX put and a short at-the-money VIX call. It gives example option Greeks and a historical VIX-to-SPX beta, then applies that beta to estimate a combined delta. The author questions whether the result implies simultaneous long exposure to the index and volatility, and whether the vega and theta arithmetic is valid.

The material is a setup for a risk-measurement question, not a worked solution. In particular, it does not resolve how to translate VIX option sensitivities into SPX-equivalent exposures or establish that a historical beta is appropriate for that purpose. Its example highlights that Greeks quoted against different underlyings cannot be combined without a carefully specified conversion and consistent units. The document offers no empirical test or definitive combined Greek, so the calculations should be read as tentative rather than as a validated hedge method.

Key ideas

• The example combines a long SPX put with a short VIX call and compares their stated Greeks.
• The proposed delta adjustment uses a historical VIX-to-SPX beta.
• The author questions whether the calculation implies inconsistent directional and volatility exposures.
• The document does not establish how to convert sensitivities across the two underlyings.

Tags

# Calculating greeks for a combination of SPX and VIX options


# Calculating greeks for a combination of SPX and VIX options












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.