2.

Question 2 (10 marks)

Kevin is investigating the performance of XYZ shares. He believes that for a given 3-month period, the probability of the share price increasing by 10% (i.e., 1.1) is 60% and the probability of decreasing by 10% (i.e., 0.9) is 40%. The current price of one XYZ share is $30.

a) Calculate the expected value of the XYZ share price after 3 months.

[1 mark]

b) Consider the number of times the XYZ share price increases in the next 1 year. What distribution should you use to model this? What values should you use for the

parameters of the distribution?

c) Calculate the mean and variance of the distribution in part (b).

[3 marks] [2 marks]

d) Estimate the probability that the share price will be lower than $38 after 1 year. Do

NOT use the normal approximation.