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Case 3: Asset Returns Assume an asset's price changes following the stochastic process: Atto Pe = Penjelas)actow = where Pt and Pt-1 are the asset's price at time t and t - 1; u is the mean of periodic return; o is volatility of periodic return; and wt is a Wiener process. (1) The parameters are calculated based on S&P500 daily data (Adj Close price) for the period 1/3/2000 - 3/7/2022. Parameter Value M 0.019% 1.239% 0 Assuming the initial asset price Po = $50 and At = 1 (i.e., daily), simulate 100 paths with 252 steps each (one year). When At = 1, the Wiener process wt is simplified as ON(0,1), which can be achieved in excel as: (8 points) ON(0,1) = 0 X NORMSINV(RANDO). (2) Calculate the mean path" of the 100 simulated paths and draw it in a scatter plot. (2 points) (3) Calculate the daily return of the asset price based on the mean path constructed in (2) following: rt = In (). Pt-1 What is the mean and volatility (i.e., standard deviation) of the asset's simulated daily return? (2.5 points) Case 3: Asset Returns Assume an asset's price changes following the stochastic process: Atto Pe = Penjelas)actow = where Pt and Pt-1 are the asset's price at time t and t - 1; u is the mean of periodic return; o is volatility of periodic return; and wt is a Wiener process. (1) The parameters are calculated based on S&P500 daily data (Adj Close price) for the period 1/3/2000 - 3/7/2022. Parameter Value M 0.019% 1.239% 0 Assuming the initial asset price Po = $50 and At = 1 (i.e., daily), simulate 100 paths with 252 steps each (one year). When At = 1, the Wiener process wt is simplified as ON(0,1), which can be achieved in excel as: (8 points) ON(0,1) = 0 X NORMSINV(RANDO). (2) Calculate the mean path" of the 100 simulated paths and draw it in a scatter plot. (2 points) (3) Calculate the daily return of the asset price based on the mean path constructed in (2) following: rt = In (). Pt-1 What is the mean and volatility (i.e., standard deviation) of the asset's simulated daily return? (2.5 points)

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