Why would you expect bitcoin to stabilize? I see no mechanism that would do that. Gold has had thousands of years of use as money-like instrument, and only periods of relative (nominal) stability during the last century or so have been when there have been organizations (central banks) to keep that stable.

http://www.macrotrends.net/1333/historical-gold-prices-100-y...

(be sure to play around with the "inflation adjusted" checkbox)

Yes, cryptocurrency prices will stabilize when they displace all fiat currencies ;) Because, until they do, they'll be too damn attractive for speculative investors to resist. That was part of the original plan, as I recall from discussion in various cryptoanarchist forums.