any views on whats the best way to trade cointegrated vol series? is it via a straddle pair, vol/var swap pair, or spread options? or sommin else?

straddles work for me

that's actually a great question. It looks indeed that despite the fact that the concept is already more than 20 years old, cointegration has not succeeded to be an operational trading methodology. Looks like correlation is still the " king" if measure of dependence regardless of all its flaws ( may be copulas are used more often in credit derivatives).But I am curious to know how did you find the 2 vols series to be cointegrated at first place: usually vol series are somewhat mean reverting, hence I(0), so how can you find a linear combination of lower order of integration ?

the real problem in my opinion is the actual trading cost. i tried two years ago to trade relative volatility within a pretty well cointegrated basket: us banks. we stopped it since we had to accept that we had actual cost of up to six vola points to set up our trades, roll them, rehedge and so forth. we did it with very little money and other people will get much better terms. i find this the biggest obstacle in trading relative vol. we did it with straddles. your options will have similar maturities, so the relative game should not require time spreads. good luck to you. i do not anyone who uses cointegration without another edge. we spend half a year and could not make it run.peace

thanks all. Cointegrating model seems marginally better than other methods....tried messing around with copulas also...all pretty much select same trade signals for moves in rel vol.but yea the big problem is trading costs. Ive never tried var/vol swaps, or spread options...just straddles/strangles, so was just curious about others experience.

QuoteOriginally posted by: veselany views on whats the best way to trade cointegrated vol series? is it via a straddle pair, vol/var swap pair, or spread options? or sommin else? well,i' have an even more fundemental question . . .what is a co-integrated vol series anyway? yes, i may indeed believe that NYMEX WTI implied vol should be cointegrated with IPE Brent implied vol. but everything i've ever read on co-integration has dealt with prices or returns! is it as simple as squaring daily returns and running the same co-integration test one runs on returns? can one just look at the implied vols and just run the co-integration tests one would run on returns?i don't know enough about it to be sure, but my gut tells me that both actual daily return vol's and daily impled vol's violate some key distributional assumption of co-integration testing . . . .as to trading correlation or covariance, modesty prevents me from posting a specific url / link . . . but you might want to google the phrase "commodity covariance contracting"

Tonyc that is exactly what I meant when asking how can Vesel find cointegration between I(0) series-- that is stationary series , and most of the time vol will be I(0)-- since vol is most of the time mean reverting, except may be if you are working with very high freq data. On one of your other point, it is only at a very basic level that cointegration only involves regressing one return series on the other.I think vesel meant to talk about is actually simply correlation ( cointegration sound a little bit fancier, but one should know I guess the basic definition...)

QuoteOriginally posted by: DogonMatrixthat's actually a great question. It looks indeed that despite the fact that the concept is already more than 20 years old, cointegration has not succeeded to be an operational trading methodology. Looks like correlation is still the " king" if measure of dependence regardless of all its flaws ( may be copulas are used more often in credit derivatives).But I am curious to know how did you find the 2 vols series to be cointegrated at first place: usually vol series are somewhat mean reverting, hence I(0), so how can you find a linear combination of lower order of integration ?Is this a case of "To a man with a hammer, everything looks like a nail", or is there something we missed?

To make the answer meaningful, I assume the cointegration effect is much stronger than correlation effect, including lagged correlations and factor correlations. That is, we have two assets whose volatilities tend to revert to a mean relation more than would be suggested by their individual mean reverting behavior, simultaneous movements and dependence on common factors; but neither one consistently leads the other. If either of those things are true, there are obvious trading strategies.To keep it simple, assume the cointegration coefficient is 1, so the two volatilities tend to the same value. I notice that one is greater than the other, so I expect convergence. I put a delta neutral short option position on the higher volatility one and a delta neutral long option position on the lower volatility; balanced so that I am unaffected by equal shifts in both volatilities or passage of time. While my cointegration model tells me this should make money, it tells me nothing about the short-term tendencies. Losses are as likely as profits. That's going to make a risky position, even if I'm right, and one that is hard to manage because I don't know anything about the timing.Therefore, I think cointegration makes sense for a long-term investor with small or moderate leverage. This investor can afford to buy cheap options and write expensive ones without worrying about short-term fluctuations or precisely balanced positions.

Aaron with all due respect given your senior member status/ number of very insightfull posts. I think there are a couple of wrong statements on your last post.**To keep it simple, assume the cointegration coefficient is 1, so the two volatilities tend to the same value. I notice that one is greater than the other, so I expect convergence**First in a cointegration framework we are talking about a cointegration vector not coefficient. Precisely the vector that will transform two apparently random variables ( with unit root), into a stationary variable ( essentially cancelling out the common stochastic trend present in both of the variables, and finding a linear combination that is stationary --- stationarity meaning here finite moments if we consider the case of strong stationarity-- ) . And if ever we can find such a cointegrating vector , what is of interest is the behavior of the residual that we got from estimating that vector. It is the mean reverting behavior of the residuals that is of interest, the speed of mean reversion -- usually determined by the autoregressive coefficient of the residuals that we would then have modelled as a AR(p) process--of the residual that will determine how fast the two variables are pulled back toward their cointegration/ equilibrium relationship. So it not the cointegration vector that determine the speed of mean reversion but the error term autoregressive coefficient.Second, techinicaly you can't talk about cointegration when the two series you are looking at are already stationary, like most vol series will most likely be. That doesn't mean that you can't model convergence of two vol series. But just don't call it cointegration. Cointegration only make sense when there is non-stationarity.Third, you said **it tells me nothing about the short-term tendencies**. That also is not quite true. If you formulate cointegration in an error correction framework, then you will have both short and long term dynamics.Bottom line, there is not a simple transposition of correlation intuition to cointegration. Cointegration is very precisely defined under precise assumptions. And a much richer concept

No need for respect.While I don't disagree with you, I think you are making things a lot more complex than necessary for the original question. Certainly you can have a cointegration vector instead of a single coefficient and we can layer an ARIMA model on top of the cointegration. But I prefer to give a simple answer to a simple question. Once you understand the simple case, you can worry about applying the insight to more complex cases.I certainly agree it is silly to cointegrate stationary series, any linear combination will work. However, I don't see anything in my post that suggests doing that. As a practical matter, people cointegrate to get better predictions, not to eliminate nonstationarities. That's a mathematical criterion that happens to lead to sensible procedures.I disagree that you volatility time series will be stationary, I think they typically violate all three stationarity conditions. Moments are often infinite, as the underlying price series has jumps. The expected values and autocovariances are nonconstant.I'm not sure what you mean by:QuoteIf you formulate cointegration in an error correction framework, then you will have both short and long term dynamics.I think it's related to your earlier statement:Quotewhat is of interest is the behavior of the residual that we got from estimating that vector. It is the mean reverting behavior of the residuals that is of interest, the speed of mean reversion -- usually determined by the autoregressive coefficient of the residuals that we would then have modelled as a AR(p) process--of the residual that will determine how fast the two variables are pulled back toward their cointegration/ equilibrium relationship.While this is a reasonable approach, use cointegration to preprocess the data before applying correlation-based methods, it's still the covariance methods that give you the short-term dynamics.I said before that cointegration is useful to a long-term, moderate-leverage investor; not a typical trader. I will amend that to say that cointegration might be useful to a trader as part of a larger analytic process.

Well about Error Correction. There used to be ( probably 10 years ago or more) 2 schools of thought in estimating cointegration relationships. Either you do it with a single equation, regress one series on the other, and check the residuals. This has been swept away by--the estimates just have better propertties-- , lets call it the system of equations approach ( Engle- Granger(1987)), where we estimate the cointegration vectors in a system of equations. Entering the system of equations are both the cointegration/ long term relationship to be estimated, and the short term relationships between the variable ( lagged differenced variables). So an Error Correction Cointegrated model both model the short and the long term dynamics between the series. That's what I meant. Volatility with infinite variance ?

QuoteOriginally posted by: DogonMatrixthat's actually a great question. It looks indeed that despite the fact that the concept is already more than 20 years old, cointegration has not succeeded to be an operational trading methodology. Looks like correlation is still the " king" if measure of dependence regardless of all its flaws ( may be copulas are used more often in credit derivatives).But I am curious to know how did you find the 2 vols series to be cointegrated at first place: usually vol series are somewhat mean reverting, hence I(0), so how can you find a linear combination of lower order of integration ?a good answer would have been fractional cointegration/long memory vol process

Quotea good answer would have been fractional cointegration/long memory vol processDogonMatrix would you care to elaborate on this with reference to the original question about how to trade on cointegrated series. After all we are still talking about comovement and not convergence in the mean even with fractional integration.