I think its actually quite stable at this point. Most of what you see now are small fluctuations due to limited liquidity and also some fake price fluctuations due to weird price reporting and suspicious (most likely fake) volume reporting by crypto exchanges.

The stabilizer has its own methods of calculating the price and what I see in the logs is mostly a percent or two of fluctuations and very short divergences of more than that when there are big market displacements (big Bitcoin crash, for example). The latter are often resolved within a few minutes.

There are pumps that take longer to resolve, but eventually that too will stop, because most who participate in them lose money.

It's certainly nothing like SBD. Even the pumps are vastly smaller: The recent pump was mostly at $1.20, while SBD pumped to $10 or so. The previous HBD pump (to $2-3) was before Hard Fork 25 in June that added collateralized conversions from HIVE to HBD. It's much harder (and costlier) to pump after that fork.