Volatility of a stock follows a GARCH$(1,1)$ model with the following parameters: $\backslash$omega $=0\mathrm{.}000075,\backslash$alpha $=0\mathrm{.}2,\backslash$beta $=0\mathrm{.}77.$ The previous stock$$s variance was $0\mathrm{.}0025.$ The previous stock price was $$40$ and the price today is $$36.$ The equation for GARCH$(1,1)$ is $\backslash$sigma $^2\_$t $=\backslash$omega $+\backslash$alpha $*\backslash$epsi $^2\_\{$t$-1\}+\backslash$beta $*\backslash$sigma $^2\_\{$t$-1\}.$

What is the long$-$run annualized volatility of the stock?

a$.5\mathrm{.}48\%$

b$.5\mathrm{.}00\%$

c$.17\mathrm{.}32\%$

d$.54\mathrm{.}77\%$