$2.$b$)$ A financial derivatives trader is attempting to judge whether an option$$s premium is cheap or expensive. For this purpose, she employs GARCH $(1,1)$ model to forecast volatility. The particular model she estimates has an intercept term equal to $0\mathrm{.}000005,$ a parameter estimate on the latest estimate of variance of $0\mathrm{.}85,$ and the parameter estimate on the latest innovation of $0\mathrm{.}13.$ The latest volatility estimate from the model were $2\mathrm{.}2\%$ per day. The option$$s underlying asset at the close of trading yesterday was $734$ and its closing price today is $756.$

i$.$ What is the new volatility estimate?

ii$.$ What is the long$-$run $($average unconditional$)$ volatility? Explain its meaning.

iii. Calculate the volatility persistence of the above returns. Explain its meaning.