The GARCH(1,1) model updates the variance using the following formula: $\sigma_n^2 = \omega + \alpha u_{n-1}^2 + \beta \sigma_{n-1}^2$

Given the parameters:

• $\omega = 0.000032$
• $\alpha = 0.12$
• $\beta = 0.8$
• $u_{n-1} = -5\% = -0.05$ (recent return)
• $\sigma_{n-1} = 2.7\% = 0.027$ (most recent volatility)

Substituting the values into the formula: $\sigma_n^2 = 0.000032 + 0.12 \times (-0.05)^2 + 0.8 \times (0.027)^2$ $\sigma_n^2 = 0.000032 + 0.12 \times 0.0025 + 0.8 \times 0.000729$ $\sigma_n^2 = 0.000032 + 0.000300 + 0.0005832$ $\sigma_n^2 = 0.0009152$

The updated volatility is the square root of the updated variance: $\sigma_n = \sqrt{0.0009152} \approx 0.030252 = 3.025\%$

This is closest to 3.0%.