Suppose that the level of the S&P $500$ index at close of trading yesterday was $$2,900$ and its volatility was estimated as $1\mathrm{.}2\%$ per day. The price at the close of trading today is $$2,800.$ Update the daily volatility estimate using:

i$.$ The EWMA model with $\backslash$lambda $=0\mathrm{.}94.$

ii$.$ The GARCH $(1,1)$ model with $\backslash$omega $=0\mathrm{.}000002,\backslash$alpha $=0\mathrm{.}05$ and $\backslash$beta $=0\mathrm{.}94.$