Volatility does not affect your rating in any way.
The only instance where volatility would come into question is when you stop playing. If your volatility is small, your deviation will increase slower than if your volatility is high. That means that you'll take more time to drop off the leaderboard.
As imperfectluck said, to lower your deviation you need to beat players that are ranked lower than you and lose against players ranked higher than you.
Also, to Kevin Garrett, it is true that if your deviation is low, your rating changes little, especially if your opponent's deviation is also low, but that's because the current rating estimate is CRE, which has this disadvantage (among others). When GLIXARE is implemented, this will still not be the case anymore. I'll explain how GLIXARE ratings work in more detail in a future thread, though.