So, you want to have an arrogant character? Well, your character has to be a sassy little sh*t, now doesn't it? The answer: Not always. Yes, your character can be sarcastic the the occasional snide and snappy remark, but not always sassy. If anything, try to have a shy arrogant character; it makes for a great plot. Also, remember this: Arrogance is where the Beautiful turn Ugly. Try to put that into a story! But, really, everything is ugly when it comes to arrogance. They ever see the bright side now do they, and when they do it's always about themselves.
Arrogant characters can also be brave and loyal characters. Yes, they think a lot about themselves (and can make great baddies!), but you read about the arrogant character that finds it in their (black and cold) heart to save someone's life; this has happened so much that readers eventually know that it's going to happen. So I suggest that you steer clear of them saving some one's life in their, but make them realize in some amazing way that they're being kind of a jackass.
this is where i ramble; have fun