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manmeet
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Volatility of Volatility

December 27th, 2010, 3:15 pm

Volatility surface based on volatility of VIX Options [backed out using VIX futures (UXA Index), Options on VIX, Black/lognormal framework] is surprizingly flat, excluding the immediate expiration and very low strikes. Given VIX follows a mean reverting pattern and has future curve resembling a physical commodity curve, I would have expected Vol surface to reflect that.I have deep interest on this topic. Any insights, papers, research surrounding this subject? Anyone trading VIX as a standalone strategy?
 
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Alan
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Volatility of Volatility

December 28th, 2010, 2:57 pm

QuoteOriginally posted by: manmeetVolatility surface based on volatility of VIX Options [backed out using VIX futures (UXA Index), Options on VIX, Black/lognormal framework] is surprizingly flat, excluding the immediate expiration and very low strikes. Given VIX follows a mean reverting pattern and has future curve resembling a physical commodity curve, I would have expected Vol surface to reflect that.I have deep interest on this topic. Any insights, papers, research surrounding this subject? Anyone trading VIX as a standalone strategy?You may be right, but on the other hand maybe the current "flatness" is not surprising.First, the VIX futures term structure is very sharply upward sloped right now. Historically, can you match up the current level and slope of the VIX futures term structureto a historical period? If so, what did the VIX smile/skew look like then? (I don't know, honest question).Second, the interaction between the mean reversion, the volatility of volatility, andthe equity-vol correlation rho, when finally run through the filter of the Black/lognormal model, is not at all obvious, at least to me.For example, take some simple models, where the instantaneous SPX variance rate V(t) (not VIX itself) follows the (risk-adjusted) sdesModel I: dV = (a - b V) dt + c V dB(t).andModel II: dV = (a - b V) dt + c V^p dB(t), (p > 1).In both cases, there is a separate price process for the SPX index level itself,and you want that one to be strongly negatively correlated to dV(t). With the volatility of V given by "c" held fixed, it might be a useful exerciseto develop the theoretical VIX futures and VIX options' implied volatility surface for the 3 scenarios:(i) flat term structure: V(0) = a/b(ii) sharp downward sloping term structure V(0) >> a/b(iii) sharp upward sloping term structure: V(0) << a/b.In case (i), we probably expect a the VIX options to show aflattish skew vs strike for model I, and an increasing skew vs strike for model II.For cases (ii), (iii), I am not so sure, and also not at all sure about therole of the equity-vol correlation rho in all of this. So, I am just suggesting a way to approach the modelling issues.
Last edited by Alan on December 27th, 2010, 11:00 pm, edited 1 time in total.
 
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frenchX
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Volatility of Volatility

December 28th, 2010, 3:40 pm

It's an interesting topic and VIX options is a hot topic in the literature for almost 5 years The term structure of VIXVolatility components: The term structure dynamics of VIX futuresI'm also prudent about the method of calculation for the VIX.
Last edited by frenchX on December 27th, 2010, 11:00 pm, edited 1 time in total.
 
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Alan
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Volatility of Volatility

December 28th, 2010, 4:15 pm

Yes, I am reminded of this very nice talk: Gatheral on VIX options