Please solve the following questions.Assume that Nikkei $225$ at close of trading yesterday was $33500$ and the daily volatility of the index was estimated as $1\mathrm{.}4$

$\%$ at that time. The level of the index at the close of trading today is $36500.$

$(1)$ Estimate of the volatility using the EWMA model with $=0\mathrm{.}94.$

The new estimate of the daily volatility by the simple return is

The new estimate of the daily volatility by the log return is

The expected daily volatility in $15$ days is

The expected daily volatility in $200$ days is

$(2)$ Estimate of the volatility using the GARCH$(1,1)$ model with $=4*{10}^{-6},a=0\mathrm{.}07,$ and $=0\mathrm{.}9.$

The new estimate of the daily volatility by the simple return is

The new estimate of the daily volatility by the log return is

The expected daily volatility in $15$ days is

The expected daily volatility in $200$ days is