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Problem 299 of 333MediumStochastic ProcessesP299
Two volatility regimes
A desk models each day's return as normal with mean 0. On a calm day the volatility is 1%, and on a stressed day it is 3%. Each day is stressed with probability 0.2, independently of everything else.
What is the unconditional daily volatility of the return? What is its kurtosis, ? (A normal distribution has kurtosis 3.)
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