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

A risk manager notes that a GARCH(1,1) model fitted to an equity index has alpha + beta = 1.00 (omega = 0). Which statement is correct about the model's forecasts?

When alpha plus beta equals one with omega zero, GARCH becomes EWMA (integrated GARCH). There is no defined long-run variance and no mean reversion, so expected future variance stays at the current level rather than reverting or decaying to zero.

  1. AForecast variance does not mean-revert; the model is equivalent to an EWMA-type process with no long-run varianceCorrect
  2. BForecast variance reverts quickly to a positive long-run level
  3. CForecast variance converges to zero over long horizons
  4. DThe model gives a long-run variance equal to omega

Explanation

With alpha+beta = 1 and omega = 0 the model is IGARCH, i.e. EWMA. The long-run variance omega/(1-alpha-beta) is undefined, so there is no mean reversion and the expected future variance equals the current variance. It does not decay to zero.

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