Question: An investor is considering purchasing a call option on the shares of Acme plc. The strike price is 300p and the option can only be exercised in exactly 2 months time. At the moment the share price of Acme is 300p.

In two months time the value of the option = Max[ shareprice − 300, 0]

During the first month the investor believes that the probability the share increases by 5% is 0.5, the probability that it increases by 2% is 0.2 and the probability the share falls by 3% is 0.3

In the second month the investor believes that the probability the share increases by 3% is 0.4, the probability that it increases by 1% is 0.3 and the probability the share falls by 2% is 0.3

Ignoring discounting, calculate the fair price for the option.

[5 Marks]