What is exactly meant by the term 'vol of vol' ? Is it the same as dvega/dvol? I have read that to be long a butterfly is to be long 'vol of vol'. Can someone elaborate on this more please? Thanks
It's the volatility of volatility, not dvega/dvol... In some stochastic vol models (e.g. SABR), it's a parameter used to quantify the "steepness" of the smile. If vol of vol is high, wings are very expensive. That may be where you're getting your fly reference.
So basically because deep otm calls/puts have positive dvega/dvol, they will benefit from volatility being volatile itself (ie. as vols go higher you make progressively more and lose progressively less when vols come off) , which isn't the case for an ATM as you always have constant vega exposure (dvega/dvol 0). This why being long fly is being long vol of vol, is that right? Do you know where i can read up more about this?
Forget dvega/dvol, that's an effect, rather than a cause... Fundamentally, it's all about vol itself being a stochastic variable. In certain models, its behavior is described by a PDE that, among others, contains a vol of vol parameter. Intuitively, this parameter in an SV model like SABR governs the "steepness" of the smile, i.e. how implied vol varies with moneyness. I always reference SABR, since I come from the world of rates, where SABR has been the de facto standard. If you have the stomach for it, the seminal SABR paper by Pat Hagan et al can be found here: http://www.math.columbia.edu/~lrb/sabrAll.pdf
I have found that people confuse two terms when talking about vol of vol. For example, the definition given above as vol-of-vol to me and probably the quantitative world is the correct one: it means the price of wings and in particular the slope of the skew/smile/smirk. So it is possible for the ATM options not to move at all, but the wings to get more expensive or cheaper. In other words, curvature. But I have also people use the term the vol of vol as it relates to VIX. So if VIX is swinging back and forth a lot, and being long a straddle or a strangle on the VIX would be profitable, they call that high vol of vol. I wish they wouldn't use the term for this. They should call that the swing of vol, or something like that.
Vol of vol is related to volatility. It just means that vol fluctuates. dvega/dvol is related to the sensitivity of a vega. There is no vega and no dvega/dvol for a S&P future for example, but prices volatility could be variable. If volatility is variable, then there is vol of vol.