Question

The parameters of a GARCH $(1,1)$ model are estimated as $\omega=0.000004, \alpha=0.05$, and $\beta=0.92$. What is the long-run average volatility and what is the equation describing the way that the variance rate reverts to its long-run average? If the current volatility is $20 \%$ per year, what is the expected volatility in 20 days?

   The parameters of a GARCH $(1,1)$ model are estimated as $\omega=0.000004, \alpha=0.05$, and $\beta=0.92$. What is the long-run average volatility and what is the equation describing the way that the variance rate reverts to its long-run average? If the current volatility is $20 \%$ per year, what is the expected volatility in 20 days?

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 23, Problem 10

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Step 1

In a GARCH(1,1) model, the long-run average volatility is given by: $$ \text{Long-run average volatility} = \sqrt{\frac{\omega}{1 - \alpha - \beta}} $$ Plugging in the given values, we have: $$ \text{Long-run average volatility} = \sqrt{\frac{0.000004}{1 - 0.05 Show more…

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The parameters of a GARCH $(1,1)$ model are estimated as $\omega=0.000004, \alpha=0.05$, and $\beta=0.92$. What is the long-run average volatility and what is the equation describing the way that the variance rate reverts to its long-run average? If the current volatility is $20 \%$ per year, what is the expected volatility in 20 days?

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