A non-dividend paying stock costs 100 at the end of today. You estimate that this stock has an expected return of 20% per year and a volatility of 50% per year. Assume that the stock return follows a Geometric Brownian motion. Consider that a year is made up of 250 trading days.

(a) Calculate the expected value of the stock price and standard deviation of the change in stock price at the end of the next trading day [4 marks]

(b) Calculate the 99% confidence interval for the stock price at the end of the next trading day. [4 marks]

(c) Calculate the 99% confidence interval for the stock price at the end of the next calendar day, i.e. consider that a year is made up of 365 calendar days. [6 marks

(d) Comment on the difference in your answer to (b) versus (c), and consider the likelihood of observing a stock price below 92 the next day. [6 marks]