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Suppose the VIX index is at a hypothetical multi-year low of 15, yet the volatility of VIX has a reading of 100. If one were to surmise from this volatility of VIX a range for the VIX over the coming period, one would have a 1-standard deviation lower bound of 0 and a 1-standard deviation upper bound of 30. This would not reflect reality, as the likelihood that the VIX would continue much lower is slim (and certainly not to 0!), while it is rather much more likely that the VIX climbs considerably beyond 30. In this sense, the 100 reading of volatility of VIX is this high because of the higher probability that the VIX could explode to the upside, and not to the downside.

How, then, does one calculate a likely range for the VIX over a given period that reflects this skew to the upside? Can one adjust the volatility of VIX reading to give more room to the upside (past 30 in our example, and at the expense of moves past 15 to the downside), or is there another, better way to construct such a range for VIX?

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