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 probability that the stock price is greater than $$42$ in one month?

a$.0\mathrm{.}74\%$

b$.99\mathrm{.}26\%$

c$.88\mathrm{.}85\%$

d$.11\mathrm{.}15\%$