I think its hard for bitcoin become stable because the price depend on supply and demand. Beside that, there is no authorities like central banks that can stabilize the price. I am believe what happen to bitcoin price is always reach new high because having limited supply and no one can intervence the price in market
You're definitely right because Bitcoin as it stands now is under no government regulations or no single body has absolute power over its price, hence Bitcoin price becoming stable seems unpracticable now. The price volatility nature is what makes holders earn huge profit when it skyrockets if the demand on the market increases.