Assume that the closing price of S&P $500$ yesterday was $1000,$ and the daily log return

volatility was estimated as $1\mathrm{.}2\%$ per day at that time using a GARCH$(1,1)$ model. The

parameters of the GARCH model are $\backslash$omega $=0\mathrm{.}000002,\backslash$alpha $=0\mathrm{.}06,$ and $\backslash$beta $=0\mathrm{.}91.$ If the

closing price of the index ends at $1015$ today, what is the new volatility estimate? $(10$

points$)$