I'm trying to reconcile an interesting brain teaser I was recently posed and I need help understanding the flaw in the reasoning.
The problem states there is an asset which after an announcement has an 80% probability of going to 100 and a 20% probability of going to 50. What is the value of an at the money call option?
The argument I was given is that the current asset price must be 90 because 90=100*.8+50*.2 and the call option value will either be 10 or 0. Then the argument tries to state the value of the option should be 10*.8+0*.2 = 8.
I know it is incorrect to use the real world probability as options are obviously priced using the risk neutral probability measure however the problem is posed in such a way that the numbers work out. The correct option price is 8 but this only works when the current asset price is 90.
Someone tried to tell me the option value depends on the probabilities which I know is not correct. What is the ultimate flaw in this reasoning? Is the flaw arguing that the asset price must be 90?
I couldn't believe my ears when a season portfolio manager was trying to tell me option prices depend on the probability of the underlying price movements and he acted confused when I tried to explain risk neutral valuation.
Any insight is appreciated.