Question: Suppose that the parameters in a GARCH(1,1) model are a = 0.04, b = 0.94, and w = 0.000003. What is the long-run average volatility?

Suppose that the parameters in a GARCH(1,1) model are a = 0.04, b = 0.94, and w = 0.000003.

  1. What is the long-run average volatility?
  2. If the current volatility is 2% per day, what is your estimate of the volatility in 30, 60, and 120 days?
  3. Suppose volatility suddenly increases from 2% per day to 3%. Estimate the effect on our volatility forecasts in 30, 60, and 120 days.

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