Gonzalez-Perez (2015) Model-free volatility indexes in the financial literature: A review makes some remarks on this topic in section 2.2.
Andersen, Bondarenko & Gonzalez-Perez (2013) identify a new error source in VIX that
generates a significant number of jumps in the volatility index unconnected with the underlying volatility process and that weakens the function of VIX as an annualized fair volatility index. This error source is related to the truncation error reported in Jiang & Tian (2005) but differs because it is generated by the CBOE rule that determines the minimum and maximum strikes considered in the volatility index formula (cutting-wings rule). After Andersen, Bondarenko & Gonzalez-Perez (2013) identify this additional error component, the CBOE added in the VIX white paper the following disclaimer: “as volatility rises and falls, the strike price range of options with nonzero bids tends to expand and contract. As a result, the number of options used in the VIX calculation may vary from month-to-month, day-to-day and possibly, even minuteto-minute.” Nevertheless, some adjustments or changes in the VIX formula should also be considered to reduce this deficiency. The literature basically suggests (i) to make the range of
strikes economically invariant and compute the VIX as a Corridor Implied Volatility (CIV)
index (see Andersen & Bondarenko (2007), Andersen & Bondarenko (2010), Andersen,
Bondarenko & Gonzalez-Perez (2013)), or (ii) extrapolate option prices in the tails using
implied volatility functions. Nevertheless, mispriced deep OTM options difficult the success of
the extrapolation exercise.
After finishing my Thesis about the subject I can provide one further interesting point: The Quality of the VIX calculation depends on the spacing of the strike prices, in terms of standard deviation of price (sd). Jiang & Tian (2005) (https://doi.org/10.1093/rfs/hhi027] find that the errors due to spacing are negligible below 0.35 sd. Regarding the range of strike prices, they find the errors due to so-called truncation of the range to be neglible beyond two sd above and below the at-the-money strike price.