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

A risk analyst fits a GARCH(1,1) model, sigma^2_t = omega + alpha*r^2_(t-1) + beta*sigma^2_(t-1), to daily returns using maximum likelihood estimation. Which statement best describes what the estimation procedure does?

Maximum likelihood estimation selects the GARCH parameters that make the observed return sample most probable given the conditional variances implied by the model. It is not a least-squares fit to the long-run variance or a matching of autocorrelations.

  1. AIt chooses the parameters that maximize the likelihood of observing the sample returns given the model's conditional variancesCorrect
  2. BIt chooses the parameters that minimize the sum of squared differences between squared returns and the long-run variance
  3. CIt sets alpha and beta equal to the sample autocorrelations of returns at lags one and two
  4. DIt chooses the parameters that make the average conditional variance equal to zero

Explanation

Maximum likelihood picks omega, alpha and beta so the joint probability (likelihood) of the observed returns, given the conditional variances the model produces, is as large as possible. It is not a simple moment match or a regression on autocorrelations.

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