2. Suppose that Barclays share price S follows a random walk: dS = Sdt+oSdX, t > 0, with S(t = 0) = So. a. Use It's lemma to find the differential equation satisfied by the variable U = In S. (3 marks) b. From this equation, find the solution for In S(1) via the variable z~ N (0,1). c. What is the expected value of U = In S(t)? d. What is the variance of U= In S(t)? e. You have invested into Barclays shares. To estimate a need for hedging, you forecast the future behavior of Barclays shares. Given So = 1171 p, = 1.3123 x 10- days , 6.0513 x 10-3 days-1/2, use table: Confidence level a 50% 95% = Za (2 marks) (1 marks) (1 marks) 0.25 0.674489750 0.025 1.959963985 to calculate the 50% and 95% confidence limits for Barclays share price S in 30 days time. (4 marks) 4 2. Suppose that Barclays share price S follows a random walk: dS = Sdt+oSdX, t > 0, with S(t = 0) = So. a. Use It's lemma to find the differential equation satisfied by the variable U = In S. (3 marks) b. From this equation, find the solution for In S(1) via the variable z~ N (0,1). c. What is the expected value of U = In S(t)? d. What is the variance of U= In S(t)? e. You have invested into Barclays shares. To estimate a need for hedging, you forecast the future behavior of Barclays shares. Given So = 1171 p, = 1.3123 x 10- days , 6.0513 x 10-3 days-1/2, use table: Confidence level a 50% 95% = Za (2 marks) (1 marks) (1 marks) 0.25 0.674489750 0.025 1.959963985 to calculate the 50% and 95% confidence limits for Barclays share price S in 30 days time. (4 marks) 4