The imprecision of volatility indexes
The paper titled, “The imprecision volatility indexes”, analyzes VVIX, the vega weighted VIX, an estimate for the 30 day expected volatility. Market participants have always wanted some kind of quantitative measure for the volatility. CBOE introduced VIX based on the Black Scholes volatility of ATM options and later changed it to a method that is based on observed option prices. The latter method in the finance literature goes by the name, “model free method”, because it uses a replicating portfolio argument of pricing a variance swap. Having said that, it is not as though it is completely “model free”, after all the risk neutral expectation of a variance swap computation assumes basic GBM with constant volatility for the stock price evolution.
What’s this paper about ?
VIX in its current avatar is plagued with a set of problems. The real world implementation of a theoretical variance swap formula gives rise to truncation and discretization errors among other type of errors. There have been some fixes proposed like natural cubic spline smoothing. The main problem with VIX is that it gives an imprecise estimate when we really want it, i.e. in times of panic. There are set of indexes for volatility that are basically tweaks around the older CBOE VXO index. In order to take care of smile and microstructure effects, there have been several suggestions of making improvements to VXO. Some of them are vega weighted VIX( VVIX), Spread weighted VIX (SVIX), volatility elasticity weighted VIX(EVIX), Transaction volume weighted VIX(TVVIX) etc. A thorough analysis of these alternative indexes is done in a paper by Susan Thomas and Rohini Grover.
This paper analyzes VVIX, an index that is a vega weighted average of Black Scholes implied volatility across strikes. The authors use NIFTY option quotes data between Feb 2009 to September 2010 for the analysis. On each day of the training data, four time instants in the day are taken for the analysis. The paper does not mention the procedure behind selecting the four time instants. I am guessing that the time instants selected are the high liquidity periods, i.e. start and end of the trading day. Or may be they were uniformly/randomly distributed during the day.
Anyway coming back to the procedure. At each time instant, a bootstrap sampling distribution of VVIX is estimated. Based on this distribution, 95% confidence bands are estimated. By using the price series, four times a day for 20 months of data, there are ~1500 data points, each of which give an estimate of 95% confidence interval for VVIX. The authors create kernel density plots based on these ~1500 data points and report the median width of CI as 2.92% and sigma of the estimate as 0.74%. If one looks at the median 95% VVIX estimate obtained, it is quite imprecise.
The paper also tries to check whether this imprecision is just a manifestation of liquidity of the underlying asset. A regression analysis is done using impact cost and the results imply a weak relationship between the width of CI and impact cost.The last section of the paper uses CI measure to select among various alternative volatility indexes such SVIX,TVVIX, VVIX and EVIX and finds VVIX is better than others.
What are the implications of the results from this paper ?
VVIX, an alternative volatility indexes, is imprecise in its measurement. This means that on a majority of days, a market participant does not really know whether the true unknown volatility has gone up or gone down. SVIX which was shown in this paper to be a good estimator of realized volatility , ranks behind VVIX based on CI measure as a model selection criterion. This means SVIX is imprecise too. CBOE, NSE and many stock exchanges in the world follow VIX that is “model free” and the VIX formula used has its own set of problems and is imprecise.
So,where are we ? The alternative volatility indexes are imprecise. The volatility indexes currently being used are plagued with problems. What’s the way out ? I guess we will have to wait until someone figures out a better volatility index that takes care of many issues of the real world such as

Finite strike interval among options

Different Strike ranges for the option series at varying maturity

Illiquidity in the OTM options

Microstructure noise

Volatility Smile

Volatility evolution and Term structure of volatility
In any case, I think this is a very interesting research area for a curious mind.