What's the relationship between oil volatility and market volatility?
We know at least for the moment that oil and stock prices are intertwined. That won't last forever, of course. Mark Hulbert shows a much different relationship if you look back past the last decade. And hey, I'm old enough to remember when lower oil prices were considered a good thing.
What about options though? Specifically, options volatility. How close is the relationship there? Well, here's a look at the CBOE Crude Oil ETF Volatility Index (OVX), the implied vol of crude, vs. the CBOE Volatility Index (VIX). OVX data only goes back to May 2007, so we're talking about 8.5 years' worth of numbers.

They move pretty closely to each other. OVX tends to sit higher than VIX, though until 2015, VIX would catch up in the spikes. Since 2015, not so much. OVX has pretty clearly led the way, and VIX has lagged. We'd probably have VIX in the mid-30s on average now if it truly tracked the OVX spike.
Despite what the above suggests, correlation between the two hasn't moved much. Here's a 20-day rolling correlation look between one-day moves in VIX and OVX:

This ebbs and flows and never really moves over time. We're right near the all-time correlation of 0.45. So, perhaps oil and S&P 500 Index (SPX) options aren't quite as locked to each other as it seems.
I suppose there are two ways of looking at the connectivity. One is, as we noted, volatility sloshes around between asset classes. You do have oil vol at highs not seen since 2009 and there's no way that doesn't have some effect on VIX.
The other is that even though the historical correlation is about normal, it's pretty clear VIX isn't fully reacting to OVX. The bull case there is that VIX is smart and expecting OVX mean reversion. The bear case there is that we're about to get faked out by better and less volatile action in oil, and the mean reversion will involve VIX catching up to some of the OVX strength.
Disclaimer: Mr. Warner's opinions expressed above do not necessarily represent the views of Schaeffer's Investment Research