I would entirely separate the investigation and analysis of volatility and correlation between two asset classes.
Think of it this way: If volatility is extremely high then high fluctuation to both, the up and down side will contribute to the stability of high volatility. However, for correlations it makes a big difference whether the large move has been to the up or down side especially the co-variation between, lets say, Dax and Bunds. The opposite holds true as well: If return volatility suddenly decreases then that has obviously a strong impact on your realized volatility measure, but it may not affect correlations at all as long as the covariation is in line with your current realized measure. Neither levels nor historical volatility-correlation patterns have any bearing whatsoever on future relationships between volatility and correlation.
By the way annualized vols for Dax were more in the region 12%-40% over the last couple years.
In summary, its entirely by chance that you observe certain patterns of stability or fluctuation in either volatility or correlation measures but what is not by chance is the ever changing and unpredictable relationships between volatility and correlations. Only when markets as a whole are stressed through exogenous events does one observe the general pattern of higher volatility and higher correlations but that generally applies to assets within the same asset class. The opaque relationship between volatility and correlations was further evidenced in late 2008 when one could pick up dispersion structures for cents on the dollar from exotic desks who attempted to clean up the books before they were entirely dismantled and everyone fired. Not that such structures were a great trade, in fact dispersion decreased further into Q1 2009.
Example: Look at how gold traded in 2008. Every last sell-side analyst in the world predicted staggering gold prices due to the flight to safety and tangible assets. Remember, even money market funds were under assault, even your paper currency under the mattress was getting devalued. And what happened? Gold was massively dumped because of hedge fund liquidations. I know a lot of volatility desks that have been long-term profitable. But to be very honest with you, I hardly ever saw a correlation desk that survived for longer than 5 years. If history has taught me personally one thing then it is that I would not bet a single coin on correlation predictions, at least a lot less than what I at times wager on direction and/or volatility.