You have been tracking the performance of a small tech company, Alpha Inc. In 6 months' time, the company will announce the result of its current research project, whether it is successful or not. You speculate the share price of the company will increase at that time as you have heard rumours that the research project is going very well.

To profit from the speculation, you decide to purchase at-the-money 6-month call options on Alpha Inc. The current share price is $13. The company is not expected to pay any dividend in the next 6 months. The risk-free rate per 3 months is 1.5% compounded quarterly and is constant in the next 6 months.

Part 1 (9 marks):

Use the risk-neutral probability method and answer questions (a) and (b). For this part only, assume that in any 3 months, the share price can either go up by 25% or down by 20%.

(a) Draw the two-period binomial tree. In the diagram, label the corresponding time period, the share price at each node and the option payoffs in the last period.

(b) Calculate the value of the call option at t=0 using the risk-neutral probability method.