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

Compared with an EWMA model with lambda = 0.94, a GARCH(1,1) model with omega > 0 and alpha + beta < 1 differs mainly in that it:

GARCH(1,1) with a positive omega and persistence below one pulls variance back toward a long-run level, whereas EWMA is a special case with omega of zero and persistence of one, so it has no mean reversion.

  1. AIncorporates a mean-reverting long-run variance termCorrect
  2. BAssigns equal weights to all past squared returns
  3. CGives zero weight to the most recent squared return
  4. DCannot be estimated by maximum likelihood

Explanation

EWMA is a special case of GARCH with omega = 0 and alpha + beta = 1, so it has no mean reversion. GARCH with omega > 0 adds a long-run variance anchor. Both give declining weights to past returns, both use the latest return, and GARCH is estimated by maximum likelihood.

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