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mbunea
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Posts: 50
Joined: March 26th, 2015, 11:39 am

Pricing options on VIX (volatility)

May 31st, 2022, 3:48 pm

So how do you guys price options on volatility (VIX)?  VIX is pretty much a volatility index so the current volatility IMPLIED from option prices and not some future on it. 

What formula do you use? By my knowledge is some Black model using futures on VIX and as far as I tested it fits the observed option prices pretty well.

But for funk's sake! Black-(Scholes) model assumes the underlier is a stock, hence it follows a geometric Brownian motion process with ANY price possible in the future. Almost zero or almost infinite and staying there that is.

Which is obviously completely off from the dynamics of a volatility underlier which is a mean reverting process.

Hence as an exercise in exercising my understanding of the market processes, I tried to produce a "correct" formula, using the correct underlier (variance) instead of some stock-based hack.

You can access it here, it's work in progress intended for my PhD, but that will probably never bear fruit. So knock yourself out: https://github.com/aquarians/Public/blo ... oc/vix.pdf
 
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Marsden
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Joined: August 20th, 2001, 5:42 pm
Location: Maryland

Re: Pricing options on VIX (volatility)

May 31st, 2022, 10:30 pm

Your link doesn't work, mbunea.

Just off the top of my head, you probably want something like geometric Brownian motion/lognormal future value distribution -- it is bounded below at zero and ultimately unbounded above -- but then to do something kinky with the volatility to reflect mean reversion. Without having tried it out -- I suspect it would create a computational rat's nest -- one thing I'd think about is having the variance of the future distribution grow with maybe the square root of time rather than just time. And then to have the drift assymptotically approach whatever you think is the long term median for VIX.

Bear in mind that I have never played around with VIX, and certainly not with real money.
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Pricing options on VIX (volatility)

May 31st, 2022, 11:00 pm

Well, for what it’s worth, the link actually works for me. The literature on this topic goes back at least a quarter century, Grunbichler & Longstaff, 1996, being a common reference. More recently, the rough volatility crowd has, I think, made some claims to the effect that their simple (or, at least, low dimensional parameter space) models can price Vix options along with options on the SPX. So this is not a new new thing, but quite possibly somewhere to make incremental progress.
 
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Marsden
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Joined: August 20th, 2001, 5:42 pm
Location: Maryland

Re: Pricing options on VIX (volatility)

June 1st, 2022, 2:37 pm

OK; now the link works for me.

Mysteries of the interwebs?
 
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mbunea
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Posts: 50
Joined: March 26th, 2015, 11:39 am

Re: Pricing options on VIX (volatility)

June 4th, 2022, 8:41 am

Thanks @Mardsen for comments and @bearish for the Grunbichler & Longstaff reference.