Please solve the following questions. The parameters in a GARCH$(1,1)$ model are estimated as $=5*{10}^{-6},=0\mathrm{.}03,$ and $=0\mathrm{.}92.$ The current volatility is

$2\mathrm{.}1\%$ per day.

$(1)$ What volatility should be used to price $25-$ and $150-$day options?

The volatility to price $25-$day option is

The volatility to price $150-$day option is

$(2)$ Suppose that there is an event that increases the current volatility by $0\mathrm{.}7\%$ to $2\mathrm{.}8\%$ per day. Estimate the effect on the

annual volatility in $25$ and $150$ days.

The effect on the annual volatility in $25$ days is

The effect on the annual volatility in $150$ days is

$(3)$ Estimate by how much the event in $(2)$ increases the volatilities used to price $25-$ and $150-$day options.

The volatility to price $25-$day option is

The volatility to price $150-$day option is