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Volatility that clusters · Part 4 of 4

Daily returns follow a GARCH(1,1): σt2=ω+α rt−12+β σt−12\sigma_t^2 = \omega + \alpha\,r_{t-1}^2 + \beta\,\sigma_{t-1}^2 with ω=2×10−6\omega = 2 \times 10^{-6}, α=0.08\alpha = 0.08 and β=0.90\beta = 0.90.

A colleague refits with ω=0\omega = 0 and α+β=1\alpha + \beta = 1. What changes?

  1. AThe long-run variance is still well defined, just higher
  2. BNothing important, since a persistence of 0.98 and one of 1 are almost the same number
  3. CShocks never decay: it becomes the RiskMetrics EWMA
  4. DVolatility becomes constant, since the weights now sum to one

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Volatility that clusters, part 4 of 4 · QuantMax