There is no stabilizing term in BTC. However, governments around the world will try to get involved in this huge market with their laws, regulation, tax, etc.
And it is proving the world accepting BTC slowly but surely. So I can tell, in the future, the price will go high, but not crazy.
There is no such thing as "stable" in the world of bitcoin. If it is stable, it can only become a worthless coin, fluctuating, rising and falling. It is a normal trading market and no one can judge the direction of the market. Bitcoin began to fall again yesterday because currency security was hacked to steal users. No one knew these things in advance, and no one could predict the decline of Bitcoin.