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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

A GARCH(1,1) model has alpha + beta = 0.97 and long-run daily variance of 0.0001. Which description of the term structure of forecast volatility is correct if the current daily variance is above the long-run level?

With alpha plus beta below one, expected variance decays geometrically toward the long-run level. If current variance is above that level, forecast volatility declines monotonically toward the long-run volatility without crossing it, giving a downward-sloping volatility term structure.

  1. AForecast average volatility over longer horizons declines toward the long-run volatilityCorrect
  2. BForecast volatility rises indefinitely
  3. CForecast volatility stays constant at the current level
  4. DForecast volatility falls below the long-run level before recovering

Explanation

Because alpha+beta < 1, expected variance moves geometrically at rate 0.97 per day toward V_L from above. It approaches but does not cross the long-run level, so the term structure of volatility slopes downward.

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