Stock price is $15 today. In a year, it has 50%-50% chances of going up or down. If it goes up, then 80% probability of the price being $25. If it goes down, then there is a 40% probability of price being $5 and a 60% probability of it being $0. Find the price of a call option at strike $25.
I think I should, first of all, find the value of the stock on the up branch of the tree that happens with a probability of 0.2. I don't know though how to find such value.
I thought to include in the reasoning the formulas of $p,u,d$ of the tree, but it doesn't seem to help.
This is the tree I am talking about. Nevertheless, in this problem, the tree should have only one node so $n=1$, and since the maturity is 1 year, t should also be 1, $t=1$