Financial Risk Manager Part 1

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Explanation:

The correct answer is C.

To estimate the updated volatility of AAA Holdings using the GARCH(1,1) model, we first define the components of the model:

$\omega$ (omega) - This is the constant term in the GARCH model, representing the baseline variance when no previous information is considered.
$\alpha$ (alpha) - The coefficient for the squared residual from the previous day, reflecting the immediate impact of past shocks on today's volatility.
$\beta$ (beta) - The coefficient for the previous day's variance, indicating how much of yesterday's volatility persists into today.

The GARCH(1,1) model formula to calculate today's variance ( $\sigma_n^2$ ) is expressed as:

\sigma_n^2 = \omega + \alpha \times u_{n-1}^2 + \beta \times \sigma_{n-1}^2

For the calculations:

$u_{n-1}^2$ - The squared residual from the previous period. Given a 5% drop in prices, $u_{n-1} = 0.05$ , thus $u_{n-1}^2 = 0.05^2 = 0.0025$ .
$\sigma_{n-1}^2$ - The variance of the previous day, based on a volatility of 2.7%, so $\sigma_{n-1} = 0.027$ and $\sigma_{n-1}^2 = 0.027^2 = 0.000729$ .

Substituting these values and the given parameters ( $\omega = 0.000032$ , $\alpha = 0.12$ , $\beta = 0.8$ ) into the formula, we calculate the updated variance:

\begin{aligned} \sigma_{n}^{2} & =\omega+\alpha \times u_{n-1}^{2}+\beta \times \sigma_{n-1}^{2} \\ & =0.000032+0.12 \times 0.0025+0.8 \times 0.000729 \\ & =0.000032+0.0003+0.0005832 \\ & =0.0009152 \end{aligned}

The square root of the updated variance yields the updated standard deviation (volatility):

\sigma_{n}=\sqrt{0.0009152} \approx 0.03 \text{ or } 3\%

This calculation shows that the updated volatility for AAA Holdings, factoring in the recent 5% price drop through the GARCH(1,1) model parameters, is approximately 3%.

Explanation:

The correct answer is C.

To estimate the updated volatility of AAA Holdings using the GARCH(1,1) model, we first define the components of the model:

$\omega$ (omega) - This is the constant term in the GARCH model, representing the baseline variance when no previous information is considered.
$\alpha$ (alpha) - The coefficient for the squared residual from the previous day, reflecting the immediate impact of past shocks on today's volatility.
$\beta$ (beta) - The coefficient for the previous day's variance, indicating how much of yesterday's volatility persists into today.

The GARCH(1,1) model formula to calculate today's variance ( $\sigma_n^2$ ) is expressed as:

\sigma_n^2 = \omega + \alpha \times u_{n-1}^2 + \beta \times \sigma_{n-1}^2

For the calculations:

$u_{n-1}^2$ - The squared residual from the previous period. Given a 5% drop in prices, $u_{n-1} = 0.05$ , thus $u_{n-1}^2 = 0.05^2 = 0.0025$ .
$\sigma_{n-1}^2$ - The variance of the previous day, based on a volatility of 2.7%, so $\sigma_{n-1} = 0.027$ and $\sigma_{n-1}^2 = 0.027^2 = 0.000729$ .

Substituting these values and the given parameters ( $\omega = 0.000032$ , $\alpha = 0.12$ , $\beta = 0.8$ ) into the formula, we calculate the updated variance:

\begin{aligned} \sigma_{n}^{2} & =\omega+\alpha \times u_{n-1}^{2}+\beta \times \sigma_{n-1}^{2} \\ & =0.000032+0.12 \times 0.0025+0.8 \times 0.000729 \\ & =0.000032+0.0003+0.0005832 \\ & =0.0009152 \end{aligned}

The square root of the updated variance yields the updated standard deviation (volatility):

\sigma_{n}=\sqrt{0.0009152} \approx 0.03 \text{ or } 3\%

This calculation shows that the updated volatility for AAA Holdings, factoring in the recent 5% price drop through the GARCH(1,1) model parameters, is approximately 3%.

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recent 5% drop in prices of AAA Holdings on the firm’s portfolio VaR. To estimate the effect, he wants first to calculate the updated volatility of AAA holdings using the GARCH(1,1) model. Tompson knows that the most recent and the long-term daily volatilities of holding are 2.7% and 2%, respectively. He also estimates the model’s parameters as: $\alpha = 0.12; \beta = 0.8$ ; and $\omega = 0.000032$ What is the updated volatility estimate of AAA Holdings?

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Last updated: June 16, 2026 at 04:31

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