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

Which statement about GARCH(1,1) parameters is correct?

A GARCH(1,1) model is mean-reverting with a finite long-run variance only when alpha plus beta is below one. Alpha governs reaction to the latest shock, beta governs persistence of past variance, and at a sum of one the model becomes IGARCH without mean reversion.

  1. AThe model is covariance stationary and mean-reverting only if alpha + beta is less than oneCorrect
  2. BA larger beta makes variance respond faster to yesterday's return shock
  3. CIf alpha + beta equals one the model has a finite long-run variance equal to omega
  4. DAlpha measures the persistence of variance and beta measures the weight on the long-run variance

Explanation

Stationarity with a finite long-run variance omega/(1-alpha-beta) requires alpha+beta<1. Larger alpha, not beta, increases reaction to shocks. At alpha+beta=1 (IGARCH) there is no finite long-run variance and no mean reversion.

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