DOPTIOTOPOTE 2. Monte Carlo Simulation of Mean revision return (20 points) Mean reversion is a financial theory suggesting that asset prices/returns eventually return back to the long-run mean or average of the entire dataset. The discrete-time mean-reversion process is a stationary first-order autoregressive process, AR(1). Specifically, the mean-reversion process can be expressed as: |(1-e-2nAt) rt = rt-1e-nat + f(1 - e-nat) +0 -N(0,1), 2n where rt and rt-1 are the return at time t and t - 1; n is the mean-revision speed; At is the step size; o is the volatility; and N(0,1) is the standard normal with mean 0 and standard deviation 1. (1) Based on the assume parameters below, simulate 100 paths with 120 steps each. (10 points) N(0,1) is realized in excel by the built-in function = norm. s. inv(rand()). FIN 470 Parameter Value 3.25% 2.5% 1.5% 1/12 3.15% (2) Calculate the mean and standard deviation for each path. (5 points) (3) Compute the "average path" based on the simulated 100 paths. Draw the "average path" in a scatter plot. (5 points) At DOPTIOTOPOTE 2. Monte Carlo Simulation of Mean revision return (20 points) Mean reversion is a financial theory suggesting that asset prices/returns eventually return back to the long-run mean or average of the entire dataset. The discrete-time mean-reversion process is a stationary first-order autoregressive process, AR(1). Specifically, the mean-reversion process can be expressed as: |(1-e-2nAt) rt = rt-1e-nat + f(1 - e-nat) +0 -N(0,1), 2n where rt and rt-1 are the return at time t and t - 1; n is the mean-revision speed; At is the step size; o is the volatility; and N(0,1) is the standard normal with mean 0 and standard deviation 1. (1) Based on the assume parameters below, simulate 100 paths with 120 steps each. (10 points) N(0,1) is realized in excel by the built-in function = norm. s. inv(rand()). FIN 470 Parameter Value 3.25% 2.5% 1.5% 1/12 3.15% (2) Calculate the mean and standard deviation for each path. (5 points) (3) Compute the "average path" based on the simulated 100 paths. Draw the "average path" in a scatter plot. (5 points) At