# Valuing an option when we have a view on future price of underlying

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.

• If you have a predicted distribution of the underlying, then the corresponding option price (undiscounted) according to that prediction is just the integral of the payoff and the distribution.
– will
Sep 25, 2017 at 21:15
• I think that makes a lot of sense. Would you discount the option back using a rate derived from the variance of the distribution? Sep 25, 2017 at 21:30
• that depends on your model, but given your question I doubt it.
– will
Sep 25, 2017 at 21:32
• How would you discount the undiscounted option value back to today? Intuitively it seems to me that the bigger the variance of the underlying price prediction is, the less valuable the option would be today since the risk would be higher. Sep 25, 2017 at 21:37
• I think you need to do some reading on the topic. The reality is that options increase in value as you increase the volatility, which makes sense when you think about the integral i mention in my comment. as for discounting it back to today, it is not related to the variance, it is to do with the value of having money now vs. having it in the future. I i can invest £95 now in a product that will pay me £100 in 1 year (i.e. a zero coupon bond), then if the expected value of your option comes out to £20 in one year, then today that is worth £20 * £95/£100 = £19 today.
– will
Sep 25, 2017 at 21:41