It's not even close to being stable, it's stable compared to before but for a supposed ''currency'' it's far from stable. The EUR or USD is stable, bitcoin is not, not even now. This wont last much longer either, we will see a break eventually either up or down.
Bitcoin is really volatile and being stable is just few times but not much longer. It won't even be stable but drops eventually when there is much supply in the market. Bitcoin is different from other currency that is why many are expecting for gaining profit from it when you are holding it until the price increase on the market.