I'm new to options trading so if this question does not make sense or is stupidly easy please bear with me. I'll try to show my thought process through an example.

XYZ  is currently trading at $100. I buy a deep  out-of-the-money contract of XYZ at a strike price of $120 for $.06 (.06*100) = $6, with 3 weeks until expiration. If XYZ shoots up to $115 the next week, will I be able to "sell" my contract back for a profit (say premium is now $.12)? Or can I not sell an OTM contract until it is ITM?