Description

FE-542
Problem 1 (50pt)
Suppose that the monthly log returns, in percentages, of a stock follow the following Markov switching model:
if st = 1 if st = 2
where the transition probability are
P(st = 2 | st−1 = 1) = 0.2, P(st = 1 | st−1 = 2) = 0.1.
Suppose that = 50, and s100 = 2 with probability 1.
(i) What is the 1-step-ahead volatility forecast at the forecast origin t = 100?
(ii) If the probability of s100 = 2 is reduced to 0.75, what is the 1-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 to simulated results.
Problem 2 (50pt)
In R create a report in pdf format using RMarkdown (or, if you choose to use Python instead, create a Jupyter notebook) to:
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Note: Let rtn denote a time series in R. To create a direction variable for rtn, use the command drtn = ifelse(rtn > 0, 1, 0)
2