FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
Which statement about the parameters of a GARCH(1,1) model is correct?
A GARCH(1,1) model is stationary with mean reversion only when alpha plus beta is below one, because the long-run variance omega/(1 - alpha - beta) must be finite and positive. At a sum of one, variance has no mean reversion.
- AA higher beta makes volatility shocks decay more quickly toward the long-run level
- BThe model is stationary and mean-reverting only if alpha + beta is less than 1Correct
- CIf alpha + beta equals 1 the model has a finite long-run variance equal to omega
- DA higher alpha makes the variance estimate less responsive to the latest return
Explanation
Mean reversion to a finite long-run variance requires alpha + beta < 1, since V_L = omega/(1 - alpha - beta). Higher beta increases persistence, not decay speed. Higher alpha raises responsiveness to the latest return. At alpha + beta = 1 (IGARCH) there is no finite long-run variance and no mean reversion.
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