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Is there a way to back into Vol of Vol for Option Pricing

March 21st, 2019, 3:42 pm

Hello,

My understanding is that stochastic option models have a IV that is stochastic and is defined by mean IV and SD of IV.  Is there a way to back into the implied distribution of IV, given market prices, just like we can back into IV itself from market prices.  Basically, how do I find the vol of vol implied by the market?

I guess conceptually, I can probably create a program that just trial/error vol of vols on the regular BS model until I get market prices.  I'd assume that would be computer intensive tho.  Just wondering if there was a way out there already.

Thanks!
 
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Alan
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Re: Is there a way to back into Vol of Vol for Option Pricing

March 21st, 2019, 6:46 pm

The closest thing to what you want might be the VVIX.

Crudely, you can interpret the current VIX as an at-the-money IV for a 30-day SPX option available today, plus a constant, say 3%. 

Thus, and again this is very crude, you could then interpret the VVIX as the market's expectation of an annualized standard deviation of the at-the-money IV to prevail in 30 days (as the extra 3% add-on won't matter for that). 

Better, but more work for you, would be to use the VIX options expiring in 30 days to produce the market's implied (risk-neutral) probability density for VIX(T), via Breeden-Litzenberger. Then, given that density, it would probably be routine to calculate the standard deviation of VIX(T). I show some plots of that density on pages 160, 162 of "Option Valuation under Stochastic Volatility II". One caveat is that the distribution has a wide right tail, so it would only be "routine to calculate .."  if the second moment of that pdf exists. I don't recall if I checked that or not. (We know the VVIX exists, but that's a different calculation).