No. It's not possible that price of BTC will be stable. And why do you want the stable price?
Not even avocados or tomatoes have never been stable. How many time producers have been obliged to trash out their vegetables just because they didn't even worth the effort implied in the harvest?
Well, I understand somehow people believe the money as something "stable". But just take a look at the dollar on the past 3 years: it has been dancing as a newbie ice-skater.
There´s no such a thing as "stable" on economics. And I´m afraid there are not going to be. BTC, as a whole new system of "money", is going to be "dancing" for years and, for sure, it will never become something static (as the dollar, euro, Yuan, &.co have never been).