Problem 1 {50pt) Suppose that the monthly log returns, in percentages, of a stock follow the following Markov switching model: Tt=1+rh at=atft1 52 = .1a_1 + 0.85311 if st = 1 * 5 + mail + User;1 if s; = 2 where the transition probability are 113(31 = 2 | ski = 1) = 0.1, ll'(s,g = 1 | s_1 = 2) = 0.2. Suppose that {1100 = 5, of\") = 53, and 3100 = 2 with probability 1. (i) 1illurliat is the 1-step-ahead volatility forecast at the forecast origin t = IUD? (ii) If the probability of 3100 = 2 is reduced to 0.9, what is the I-step-ahead volatility forecast origin t = 100. Bonus In R create a report in pdf format using RMarkdown (or, if you choose to use Python instead, create a Jupyter notebook) to implement this Markov switching model and compare the forecasts you computed in (i) and (ii) to simulated results with at least 1000 simulations