$($Risk Management and Financial Institutions$),($Financial$),($ algebra $)$ Forecasting Volatility

A few lines of algebra shows that, for the

GARCH$(1,1),$

$E[{}_{n+t}^2]=V_L+(+{)}^t({}_n^2-V_L)$

To estimate the volatility for an option

lasting $T$ days we must integrate this from

$0$ to $T$