1. Consider a stock price S(t) modeled by the generalized Wiener process d(In S) = vdt + odz (a) (2pts) What are E[ln S(t)) and var[ln S(t)]? (b) (4pts) Using At = 1/12, v = 0.1, 0 = 0.5, and S(0) = 10, use the simulated outcomes for the standard normal random variable e shown in the table below to simulate the stock price up to t = 1/3 years. Keep at least 4 significant figures in your calculations (eg 1.430 or 0.08733). Summarize the results here: t S In S 1.68 -1.29 -0.42 0.28 -1.58 (c) (2pts) Evaluate E[In S(1/3)] and var[ln S(1/3)] from part (a) for the parameters in part (b). (d) Are the results from part (b) and (c) consistent? Explain. 2. (5pts) A stock price S(t) is governed by ds = aSdt + bSdz where z is a standard Wiener process. Use Ito's lemma to find the process that governs G(t) = S2. 1. Consider a stock price S(t) modeled by the generalized Wiener process d(In S) = vdt + odz (a) (2pts) What are E[ln S(t)) and var[ln S(t)]? (b) (4pts) Using At = 1/12, v = 0.1, 0 = 0.5, and S(0) = 10, use the simulated outcomes for the standard normal random variable e shown in the table below to simulate the stock price up to t = 1/3 years. Keep at least 4 significant figures in your calculations (eg 1.430 or 0.08733). Summarize the results here: t S In S 1.68 -1.29 -0.42 0.28 -1.58 (c) (2pts) Evaluate E[In S(1/3)] and var[ln S(1/3)] from part (a) for the parameters in part (b). (d) Are the results from part (b) and (c) consistent? Explain. 2. (5pts) A stock price S(t) is governed by ds = aSdt + bSdz where z is a standard Wiener process. Use Ito's lemma to find the process that governs G(t) = S2