As a risk manager, your task is to evaluate the downside risk of a given asset. In particular, you need to compute the Value at Risk (VaR) for the SPY ETF based on the period dating between Jan 2017 and Dec 2021. To do so, you need to perform the following tasks: (a) To get started, you need to work with weekly adjusted closing prices. The total time series should correspond to 261 weeks. Based on this data, calibrate the and , assuming that the asset price follows a geometric Brownian motion. Report the estimates in a table. (5 Points) (b) Given the calibrated parameters. Assume that the initial price is given by the last closing price from the week of Jan 8th, 2017. This price should be around $200s. Based on this information and Monte Carlo (MC), you need to simulate the asset price path 1000 times over 260 weeks, corresponding to five years of data. To ensure your results are correct, compute the simulated conditional expectation and variance of S5 given S0 and compare them to the true values. You should report all four values in a single table. (10 Points) Hint: recall Lab 2. (c) In reality, there was a single trajectory of how the SPY price played out during this sample period. On the other hand, the MC simulation results in 1000 paths. Clearly, out of the 1000 paths, there is one simulation that deviates the most and one that deviates least from the true trajectory. Can you spot the latter? As a summary, plot this simulated path versus the actual one. (5 Points)