# Construction of “vol of vol”

How do you construct something that lets you buy "vol of vol"? not necessarily for VIX, but any particular stock or index.

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Sounds like you're asking for compound options, which are options on options. These things are considered exotic and would have to be negotiated over-the-counter. – chrisaycock Oct 17 '12 at 19:11
yeah, but if i wanted to DIY it? how could it be done. i just wanna see how exactly it would work. – user13783 Oct 17 '12 at 19:12
I just updated my comment to have a link to an academic paper about it. – chrisaycock Oct 17 '12 at 19:12
appreciated. ty. – user13783 Oct 17 '12 at 19:14

It depends on whether the second term in "vol of vol" refers to realized or implied. If realized, I don't know. If implied, you could "DIY it" by buying straddles on a volatility product and hedging deltas with the underlying futures. There are options on VIX, GVZ (gold), OVX (oil) and the other CFE futures although only the VIX options are active.

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There are really only a few ways to trade vol of vol even in the index space. In the implied space, you can trade options on VIX. In the realized space, you can trade options on realized variance (illiquid these days) or trade var>vol spreads.

Also, vol of implied vol in equities is linked to the slope of the skew, so going long or short risk reversals is a proxy.

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This depends on your volatility model. Even for underlying like stocks, many vol models have parameter of vol of vol. And option pricing results from the model obviously have sensitivity to that parameter. Once you hedge out all the other risks (delta, vanna, vega) but leaves out the sensitivity to that parameter, by the model, pnl depends on vol of vol.

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The VIX itself is connected to a special strip of options which is sensitive to just the volatility of an underlying in a non model dependent manner. This can be performed for any underlying that has options on it, not just the S&P. There is an excellent white paper regarding it you can find on the CBOE site. VIX White Paper

You may not be aware that there is also a skew index designed to be sensitive to the third moment of an underlying's distribution. It uses a similar technique of putting together a strip of options to calculate that value. I'm sure you could repeat to produce something that is sensitive to the fourth moment, which you can think of as vol-vol. I'd also be surprised there is isn't a paper out there that has done this yet.

The answer would then be to buy those options.

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Varswap vs volswap would do the trick. Similarly, varswap vs straddle more or less accomplishes the same thing (more local wrt spot), or even a strangle vs straddle (ratio'd vega neut) as the poor mans vol of vol trade.

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