6. Let Z be a Wiener process. Given a non-dividend paying stock with expected rate of return and volatility o, assume that the stock price S follows the Ito process dS = S dt+oSaz. (2) (a) State the properties which the process Z satisfies. (b) State Ito's Lemma. (C) Suppose that a stock price has an expected return of 2.5% per annum and a volatility of 15% per annum. When the stock price at the end of a certain day is $60, calculate each of the following: (i) The expected stock price 15 days later; (ii) The standard deviation of the stock price 15 days later; (iii) The 95% confidence interval for the stock price 15 days later, (d) Find the process that is followed by the variable shl Show that sll also follows a geometric Brownian motion. (6] [8] 6. Let Z be a Wiener process. Given a non-dividend paying stock with expected rate of return and volatility o, assume that the stock price S follows the Ito process dS = S dt+oSaz. (2) (a) State the properties which the process Z satisfies. (b) State Ito's Lemma. (C) Suppose that a stock price has an expected return of 2.5% per annum and a volatility of 15% per annum. When the stock price at the end of a certain day is $60, calculate each of the following: (i) The expected stock price 15 days later; (ii) The standard deviation of the stock price 15 days later; (iii) The 95% confidence interval for the stock price 15 days later, (d) Find the process that is followed by the variable shl Show that sll also follows a geometric Brownian motion. (6] [8]