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Strike Coverage and Tail Truncation in VIX-Style Volatility Estimates

Article Quant Q&A · Author: Joker Chair
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Summary

The discussion addresses an uneven set of out-of-the-money calls and puts when estimating a VIX-style implied variance measure from commodity options. It highlights that limited strike coverage can bias the estimate downward, while widely spaced strikes can create discretization error. These issues matter because the calculation aggregates option prices across a range of strikes rather than relying only on near-the-money contracts.

The answer summarizes research findings that define adequate coverage in terms of each tail extending about 3.5 standard deviations from the at-the-money forward, with standard deviation scaled by implied volatility and time to expiry. It also reports that strike spacing below about 0.35 standard deviations makes discretization error negligible in the cited analysis. A second respondent suggests using put-call parity to infer missing puts. The exchange does not establish that parity is always usable with the available market inputs, nor does it give a full procedure for commodity-specific contract conventions or a quantitative remedy for sparse data.

Key ideas

  • Sparse option strike coverage can bias model-free implied volatility estimates downward.
  • Wide gaps between listed strikes can introduce discretization error.
  • The cited research describes tail coverage relative to the forward and volatility-scaled time to expiry.
  • Put-call parity is suggested as a way to infer prices on the underrepresented side, subject to suitable inputs.

Tags

OptionsCommoditiesVolatilityDerivatives pricing
Full text
# When calculating VIX, how to deal with the problem of asymmetry of put and call data?


# When calculating VIX, how to deal with the problem of asymmetry of put and call data?












I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the money, but there're 3 or fewer put options out of the money. How to deal with such asymmetric problem? Any suggestion or hit is helpful.

## Answer by Martin Georg Haas (score 2, accepted)

https://quant.stackexchange.com/a/78158

I have dealt with this problem in my research, here are my findings and takeaways:

- Not enough options are a problem: Jiang and Tian (2007) showed that an insufficient range of strikes leads to a downward bias in the calculated MFIV. The discreteness of strikes also introduces errors if strikes are too widely dispersed.

- How "enough" is defined: Jiang and Tian (2005) showed that reliable MFIV estimates can be obtained if the truncation point of each tail is 3.5 standard deviations (SDs, defined as multiples of $\sigma_t \sqrt{\tau}$ with $\sigma_t$ the Black&Scholes IV and $\tau$ the time to maturity) from the at-the-money forward price $F_0$. They further show that the “discretization error”, which is induced by the spacing between adjacent strike prices, is negligible below strike-price increments of 0.35 SDs.



## Answer by Lsvob (score 0)

https://quant.stackexchange.com/a/71738

This is perhaps a bit of a stretch but how about inferring the value of the puts by using the put-call parity principle?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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