I am struggling with the following:
an investor is considering a call option on the shares of XYZ. the strike price is 510p and the option can only be exercised in exactly 2 months time. at the moment the share price of XYZ is 500p. in 2 months time the value of the option = Max[shareprice-510,0]
During the first month the investor believes that the probability the share increases by5% is 0.35, the probability that it increases by 2% is 0.5 and the probability the share falls by 4% is 0.15.
In The second month the investor believes that the probability the share increases by 4% is 0.3, the probability that it increases by 1% is 0.45 and the probability the share falls by 3% is 0.25
Calculate the price the investor is willing to pay for the option assuming they want to make 3% expected return over the period.
I calculate the expected return using a tree graph (in the picture below). The result is 11.177 (summing up all the value of the option by the probabilities) and that is a return of 2.2%. (Please keep in mind that if the share price is below the strike price the value option is 0)
My problem here is that I need to get the fair price, knowing the expected return... so I need to do exactly the opposite.
What is the formula to get the price the investor is willing to pay in order to get a 3% expected return?