Could there be an edge in pricing options on volatility?

A

Aquarians

To my knowledge (asked here), the model used to price options on VIX is Black: https://en.wikipedia.org/wiki/Black_model

Which makes sense because just like my observation with options on plain stock indexes, you can't trade the index. So traders use the next best proxy, namely a future on it.

But that can't be 100% right. Right? Because the future is not the present. So I tried to figure out if there's some arbitrage opportunity in all suckers using the wrong model. Couldn't figure one so what the heck, I published my research on it: https://www.sciencepublishinggroup....?journalid=147&doi=10.11648/j.acm.20150403.24 . Got $10,000 from the Romanian state in the form of a PhD track which I haven't completed yet and probably never will.

Anywayz following my train of thought, the Black model assumes an underlier which follows a Geometric Brownian Motion (stock). That can't be further from the dynamics of the volatility options underlier, which is A MEAN-REVERTING PROCESS.

So what's the correct formula (and derivation) to use in pricing options on volatility?

I'm not aware of a Black-Sholes like formula so here's my attempt at it: https://github.com/aquarians/Public/blob/main/Aquarians/Backtester/src/main/resources/doc/vix.pdf

BTW, if there's an opportunity in that formula, that's FAR, VERY FAR eclipsed by my latest research which values in the, I'm not bragging, $1,000,000,000,000. Just have to talk to beings other than chimps about it.

Same discussion on the antithesis of this forum: https://forum.wilmott.com/viewtopic.php?f=11&t=102725
 
The short answer is yes, but they are more common than you would imagine. Not giving any investment advice, but you'll need substantial resources, a floor broker and access to the upstairs markets and lightening fast access to the futures. You'll need to be nimble and rest assured lot's of desks have the technology. Look at what Parallax discloses as Pro Customer MM.
 
No the black model isn't it but yes there is an edge and there is predictability in the premiums. You'll need to understand very advanced stuff to get it tho
 
Do you not know how to Google or what? Jim gatheral solved the joint calibration problem it calibrates perfectly to even short dated contracts
 
So here we have a post from a clueless idiot who doesnt know about rough volatility and then a like by a wanna be trader who is too stupid to recognize the value I was offering him. good luck fellas! this is not investment advice.
 
Apparently it's covered by Grünbichler & Longstaff in "Valuing futures and options on volatility" : https://www.sciencedirect.com/science/article/abs/pii/0378426695000348

Took a quick look and it's the same formula I derived myself without knowledge of their work, only I eventually got bogged down in the numerical computation of some weird-ass function: https://en.wikipedia.org/wiki/Marcum_Q-function .

In the Grünbichler & Longstaff paper they say "While this function is straightforward to evaluate, it is often more convenient to calculate its value using the highly accurate normal approximation suggested by Sankaran (1963).". First doesn't seem very "straightforward to evaluate" to me, but the normal approximation is nice, wouldn't have thought about it in a million years.

Anywayz, it's not something found easily on Google unless one knows already what to look for. And there's no Wikipedia entry whatsoever on it, like there are for more mainstream models like Black-Scholes, Merton's jump-diffusion or Heston's stochastic volatility. Someone should add it! (But not me, I'm lazy) :)
 
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