option on implied vol

sunya · March 2nd, 2005, 12:04 am

I want to price, say a 1y call on the 1y ATM implied vol. ATM is defined as of in 1y of course. What do you think is the simplest model ? BS would be a joke, but there is no really forward smile in this after all. Something warns me about local vol, but what is the problem exactly ?

PaperCut · March 2nd, 2005, 1:26 am

QuoteOriginally posted by: sunyaI want to price, say a 1y call on the 1y ATM implied vol. ATM is defined as of in 1y of course. What do you think is the simplest model ? BS would be a joke, but there is no really forward smile in this after all. Something warns me about local vol, but what is the problem exactly ?1) Call market maker2) Get price3) Be happy

erstwhile · March 2nd, 2005, 3:05 pm

I think there have been a few recent papers on general volatility derivatives. Here is a pre-print of a paper by Gatheral and Friz that might be a good starting place:

exotiq · March 2nd, 2005, 5:23 pm

There have also been lots of other papers over the years from the likes of Lipton, Pugachevsky, Carr, and others. There's a lot of math involved in vol derivatives, but I've seen few of them other than plain old variance swaps actually trade.Mathematically, such an option is a function of forward vol and vol of vol (to a specific term), which many stochastic vol models can handle about as well as they handle multiplicative cliquets or other forward-skew sensative products. If you model these risks, see how they fit in your vol book, and what types risk such a thing would leave you hedging, you're on your way...

Collector · March 2nd, 2005, 5:42 pm

>BS would be a jokeYou can get quite far with a good joke, if you understand the humor

quantstudent19 · March 3rd, 2005, 8:15 pm

QuoteOriginally posted by: exotiq There's a lot of math involved in vol derivatives, but I've seen few of them other than plain old variance swaps actually trade.Someone told me stuff like digitals or one touch on vols actually traded in greece as a convergence trade when drachma entered EMU.Is it true, or was it just plain vol swaps?

Val · March 4th, 2005, 12:11 am

QuoteOriginally posted by: Collector>BS would be a jokeYou can get quite far with a good joke, if you understand the humor ... and pay for the consequences.... ?!

probably · March 4th, 2005, 12:39 am

BS is a start (assuming you mean using BS for the vol itself not the stock).Any Asian pricer will then give you an option price.Another obvious way to go is calibrate Heston/HestonLocalVol/etc and price it that way.I've also tried a bit in the context of options on variance, and thatis what I cam up with http://www.math.tu-berlin.de/~buehler/d ... ves.pdfbut it describes more options on variance than options on implied.

Val · March 4th, 2005, 1:08 am

QuoteOriginally posted by: probablyBS is a start (assuming you mean using BS for the vol itself not the stock).Any Asian pricer will then give you an option price.Another obvious way to go is calibrate Heston/HestonLocalVol/etc and price it that way.I've also tried a bit in the context of options on variance, and thatis what I cam up with http://www.math.tu-berlin.de/~buehler/d ... ves.pdfbut it describes more options on variance than options on implied.Unfortunatly, as you know very well probably, the things look much more complicate for volatility swaps from mathematical point of view ....However erstwhile's paper with the square root mean reverting process although very interessting the formula provided by Yor, I think , I've never seen the demonstrations....

eiriamjh · March 4th, 2005, 12:16 pm

QuoteOriginally posted by: erstwhileI think there have been a few recent papers on general volatility derivatives. Here is a pre-print of a paper by Gatheral and Friz that might be a good starting place:Very interesting indeed - I always wondered whether Carr-Lee approach for pricing volatility derivatives was of any useI got the answer in the conclusion of the gatheral-fritz paper:QuoteFinally, it should be clear from the graphs of the weights that we pre-sented that this work does not concern itself with how to hedge volatilityderivatives. All we have done is to indicate how they should be priced rela-tive to the prices of European options on the underlying.Could someone kindly explain to all quants that a price is worth little if there is no hedging strategy associated to it?e.

erstwhile · March 4th, 2005, 1:14 pm

eiriamjh: to me that was like a cliff-hanger that says "stay tuned for the exciting conclusion in our next episode!"Jim Gatheral used to be head of eq deriv trading at Merrill, so is very conscious of the needs of traders.

eiriamjh · March 4th, 2005, 1:57 pm

erstwile: I m longing for the next episodenevertheless prices derived without a hedging strategy are pretty much worthless : either carr, lee, gatheral fritz et al. have an undisclosed hedging strategy to support their theory (in which case they won t be able to convince anyone until they disclose it) or they don't (in which case nobody will listen to them)a suivre...e.