The GARCH(1,1) formula for daily variance is: $\sigma_n^2 = \omega + \alpha u_{n-1}^2 + \beta \sigma_{n-1}^2$

Given the information:

• $\omega$ (Weighted long-run variance) = $0.000010$
• $\alpha$ (Weighting on previous period's return) = $0.15$
• $\beta$ (Weighting on previous volatility estimate) = $0.80$
• $u_{n-1}$ (Recent market return) = $1%$or `$0.01` \implies u_{n-1}^2 = 0.0001$
• $\sigma_{n-1}$ (Daily volatility estimate) = $1.5%$or `$0.01`5 \implies \sigma_{n-1}^2 = 0.000225$

Substituting the values into the formula: $\sigma_n^2 = 0.000010 + 0.15 \times (0.0001) + 0.80 \times (0.000225)$ $\sigma_n^2 = 0.000010 + 0.000015 + 0.000180 = 0.000205$

To find the daily volatility, we take the square root of the variance: $\sigma_n = \sqrt{0.000205} \approx 0.0143178 \approx 1.432\%$