# How does Volatility Pairs Trading work?

I've read some material related to pairs trading for equities and I understand the process of finding non-stationary pairs price series that can be cointegrated to form a stationary series. The basic idea being to trade on the oscillations about the equilibrium value of the spread. While i understand how this is accomplished with equities, i'm not sure how suitable implied volatility pairs on equity options are identified since both implied volatility series would already be stationary and so cointegration would not be required. Can someone please explain to how suitable implied volatility pairs are identified?

• Cross-posted on NP Aug 17 '14 at 20:25
• is cross posting frowned upon on message boards? i'm just trying to use all resources available to get an answer. If it is i'll remove. Aug 18 '14 at 17:11
• Different forums have different opinions. I find cross-posting without disclosing to be rude. You're asking for people's time, but do not let them know to check other forums to see if there's already a satisfactory answer. The only reason I noticed your cross-posting is because I monitor several forums' RSS feeds. Aug 18 '14 at 17:23
• Ok I got it, thanks for the response. No harm intended, I was merely trying to get an answer to something that's been frustrating me for a while. I'll remove it from NP. I did get an answer to my question on another message board, what's the proper etiquette in this situation? Should i remove from here also? or should i post a link to the answer on the other board as well. Thanks for informing me, i only post sparingly, won't do this again without disclosure going forward. Aug 18 '14 at 17:50
• If you got a sufficient answer elsewhere, you can either link to it in the comments, or answer the question yourself (but that can depend on the other forum's rules regarding who owns the content; you might be okay as long as you provide proper attribution to the original author of the answer). Aug 18 '14 at 17:59

If you believe the process $Y_t$ to be stationary, you can try to profit from it via a mean-reversion strategy or any other way that exploits the stationarity. It doesn't matter whether $Y_t$ is obtained as a cointegrational combination of a few non-stationary processes, or as a linear combination of some processes that are stationary themselves.

In the early years of the so-called Statistical Arbitrage, they never even used the formal cointegration tests because they were not available at the time. The original simple idea was to pair "similar" equities and pick the pairs with the spread that was both "stable" and looked like it had some profit generating potential. I believe a similar approach is applied to the volatility pairs.

A (very) simplistic approach is as follows: take a bunch of volatility instruments and compute the implied volatility, $v_t$ over some horizon. Then for each instrument $i$ compute the volatility increments $\Delta_t^i = v_t - v_{t-1}$. For each pair of instruments $(i,j)$, compute the "distance" between them as $[1 - correlation^2(\Delta^i, \Delta^j)]$. The pairs with the smallest distance are the ones used for trading. For each pair, when the volatility spread becomes too wide/narrow compared to the historical average, you take a bet that it will narrow/widen in the future.

If you take a look at this well known early paper on StatArb and replace the term "stock price" with "implied volatility", you'll get a better idea.

• Can you elaborate on how to determine which pairs have profit generating potential. Now the answer feels a bit unfulfilling. Sep 15 '14 at 19:08
• Hi, by differencing stationary time series you make them non-stationary which generates risk of spurious correlation - do you agree ?
– Qbik
Jan 18 '17 at 19:46
• Hi Bob: Could I make it simple and just send a big fat check to you? I certainly hope it will be quite fulfilling. Jan 20 '17 at 15:28
• Qbik: I disagree. When you difference a stationary series, you may introduce some temporal correlation (e.g. look what happens if you difference the white noise process), but I don't see why that correlation is spurious. Jan 20 '17 at 15:31