frolloos


Total Posts: 70 
Joined: Dec 2007 


How is correlation between the underlying and its volatility hedged / traded in practice? Is it important /relevant to be able to do that? Any useful rules of thumb? 




ronin


Total Posts: 457 
Joined: May 2006 


I might be misunderstanding the question, but that is pretty much the textbook definition of the skew.
How is skew traded and hedged? Call spreads and put spreads, how else. If you can't trade options, you can't hedge it.

"There is a SIX am?"  Arthur 


frolloos


Total Posts: 70 
Joined: Dec 2007 


You didn't misunderstand the question I think, but I find correlation sensitivity = skew = c/p spreads a broad or even vague concept. Which strikes, what notionals, and why?
If you are working with a specific SV model in mind, you could bump the correlation and find the sensitivity of the option or structure to the correlation parameter. Then you wouldn't necessarily have to trade the 'skew' but just another option with suitable notional, or not?
If you don't have a specific model, then how would you define correlation sensitivity of an option, and what is the mathematical relationship to 'skew' then? 




ronin


Total Posts: 457 
Joined: May 2006 


You probably want to take a step back.
Skew sensitivity of some option product is not model dependent. It is something you objectively either have or don't have, it has model independent magnitude, and it is modelindependently best matched with some combination of call and put spreads. That is all model independent.
Spot vol correlation takes that (objective) skew dependence and translates it into the language of a (subjective) sv model.
I guess it makes sense if you are trading realised spot vol correlation against the implied skew. As in, implied skew is too high so you short it and run it.
But that is the opposite of hedging it.
Bottom line, hedging the skew is model independent. Punting on the spot vol correlation is model dependent. "Hedging spot vol correlation in a model independent way" doesn't make sense.

"There is a SIX am?"  Arthur 


Strange


Total Posts: 1557 
Joined: Jun 2004 


@frolloos Are you looking for a product that specifically isolates the skew from other risks in a modelindependent way? There is nothing really common out there, though there was a time when gamma swap  var swaps were touted as a way to structure this exposure. CBOE has specified a modelindependent SKEW index and was planning to list futures on it but decided not to go down that road.
@ronin actually, it's a valid and interesting question  plenty of structured products are pitched that way. Think of it this way  a vol swap is a way to trade volatility in a modelindependent way as opposed to a deltahedged straddle which depends on your model assumptions. Similarly, a simple risk reversal does not represent pure skew risk as your pnl is gammaweighted (and thus modeldependent) but there are some structured products that supposedly do. 
Eher Ende mit Schrecken als Schrecken ohne Ende 



ronin


Total Posts: 457 
Joined: May 2006 


@strange,
Absolutely. Some sort of gammadecayingweightedaverage of call spreads would generate a "skew swap" along the lines of a var swap, with delta vanishing at all strikes. If you have clients who want something like that, go for it. It sounds very 2006 to me.
But it doesn't address the conceptual point. You can trade spotrealisedvol correlation against the implied skew. But you can't hedge it out.
Say I buy MSFT and I receive the implied MSFT skew in this skew swap. The result isn't MSFT with uncorrelated spot and vol.

"There is a SIX am?"  Arthur 


frolloos


Total Posts: 70 
Joined: Dec 2007 


@strange: I am looking to trade correlation in a (almost) modelindependent way, just like volswaps can be traded/hedged in a (almost) model independent way.
I agree with ronin that skew is fully model independent. It is what it is regardless of the underlying model. But you need a good definition of skew, at the very least it has to be zero for a smile that is fully symmetric in log moneyness. So I think skew should be defined as the difference in implied vol between opposite values of logmoneyness.
Anyway, to go back to the relation between correlation and skew (skew as I wrote it above at least):
@ronin: I am not sure I fully agree with you that hedging correlation in a modelindependent way doesn't make sense. Technically and strictly speaking you are right, but I think that as is the case for volswaps, sensitivity to correlation can be decomposed into a large modelfree part, and a small modeldependent 'basis', and I think this modelfree part can be directly related to the observable skew and traded/hedged.





ronin


Total Posts: 457 
Joined: May 2006 


I think I am getting closer to understanding what you are after. All this stuff about options is irrelevant  you just want to take a view on the third moment of spot returns?
I haven't actually taken the time to think about this in any detail. But if you put a gun against my head to come up with a strategy to do something like that, the basic idea would be something like have position q on dips and Q on peaks where Q>q. The idea being that you are trying to keep your pnl volatility constant in a skewed returns distribution. So when volatility is higher, you put on smaller quantity. And then do some sums to see how your pnl distribution depends on the third moment of spot returns, and from that work out the break even q/Q ratio at any given skew level.
The elephant in the room is that this would not be solated skew exposure. Either you would be trading it directionally (sign q = sign Q) in which case you still have delta, or non directionally (sign q \neq sing Q), in which case you have gamma. I don't see a way to get out of both gamma and delta at the same time.

"There is a SIX am?"  Arthur 

