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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.

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    $\begingroup$ @nbbo2 I understand that you mean. But is there any method to deal with such a problem? I'm tryin to calculate the VIX index of commodity options. During most time, there may not be enough option data... $\endgroup$ Jul 27, 2022 at 5:56
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    $\begingroup$ I am assuming you do not want to use CBOE's CVOL? Or is your particular commodity not included in the indices? You could also "simply" use a 1m ATM IVOL as a proxy from a vol surface, provided you have one available. $\endgroup$
    – AKdemy
    Jul 27, 2022 at 15:07
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    $\begingroup$ @AKdemy Thank you very much! I just saw the methodology of CVOL, it's very helpful! $\endgroup$ Jul 28, 2022 at 1:56

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

  1. 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.

  2. 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.

  3. The solution: Jiang and Tian (2007) proposed a smoothing method that fills gaps and extends the strike prices. You might be interested in my R-Package R.MFIV that implements the VIX calculation, quality assessment and also the smoothing method. I explained the entire derivation and calculation in this paper

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

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  • $\begingroup$ Wouldn't put call parity just give options of the same strike? This doesn't solve the issue of lack of OTM puts. $\endgroup$
    – user34971
    Jul 27, 2022 at 12:01
  • $\begingroup$ A strike which would make a call ITM makes a put OTM. I don't know how many ITM calls exist, however. $\endgroup$
    – Lsvob
    Jul 27, 2022 at 12:05
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    $\begingroup$ ITM options are generally less liquid. $\endgroup$
    – user34971
    Jul 27, 2022 at 12:07

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