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Volatility that clusters · Part 3 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.

How many days does it take for half of a shock to the variance forecast to decay, to one decimal place?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

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Volatility that clusters, part 3 of 4 · QuantMax