Financial Risk Manager Part 1

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Explanation:

Calculate the new estimate of variance: $\sigma_n^2 = \omega + \alpha u_{n-1}^2 + \beta \sigma_{n-1}^2 = 0.000005 + (0.04 \times 0.02^2) + (0.92 \times 0.01^2) = 0.000005 + 0.000016 + 0.000092 = 0.000113$ New volatility = $\sqrt{0.000113} = 0.01063$ or $1.063%$2. Calculate the implied long-run variance: $V_L = \frac{\omega}{1 - \alpha - \beta} = \frac{0.000005}{1 - 0.04 - 0.92} = \frac{0.000005}{0.04} = 0.000125$ Long-run volatility = $\sqrt{0.000125} = 0.01118$ or $1.118%$

Explanation:

Calculate the new estimate of variance: $\sigma_n^2 = \omega + \alpha u_{n-1}^2 + \beta \sigma_{n-1}^2 = 0.000005 + (0.04 \times 0.02^2) + (0.92 \times 0.01^2) = 0.000005 + 0.000016 + 0.000092 = 0.000113$ New volatility = $\sqrt{0.000113} = 0.01063$ or $1.063%$2. Calculate the implied long-run variance: $V_L = \frac{\omega}{1 - \alpha - \beta} = \frac{0.000005}{1 - 0.04 - 0.92} = \frac{0.000005}{0.04} = 0.000125$ Long-run volatility = $\sqrt{0.000125} = 0.01118$ or $1.118%$

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UAnonymous

Last updated: June 22, 2026 at 14:11

New volatility = 1.063%; long-run volatility level = 1.118%.

New volatility = 0.0113%; long-run volatility level = 0.000125.

New volatility = 1.225%; long-run volatility level = 2.5%.

New volatility = 0.0125%; long-run volatility level = 3.2%.