I have a model that predicts the future price of a stock, and would like to incorporate this information to value the option. Lets take an example. AAPL stock is trading at 151.89 US dollars today (Sep 22, 2017). I would like to compute the fair value of the call option with a strike of 149 that expires on Oct 20, 2017. From the market I can get the current mid price of the option and its implied volatility. However, lets say my model predicts that the value of AAPL on Oct 20, 2017 is normally distributed with a mean of 145 dollars and a standard deviation of 1 dollar. How could I use this information to compute the value of the option? For the purposes of this question, we can assume the dividend yield is 0 and we know the risk free rate. If somebody has a way to do this for a European option instead of an American that would probably be close enough for my purposes.
The purpose of computing the value is so I can buy or sell the option where market price is most different from the value computed above thus maximizing risk adjusted return. The assumption, of course is that my model is accurate.