# What is the formula for variance in estimating exchange rate?

I was watching this Youtube Video. He used a exchange rates of Euro to Dollar for a few days and apply GARCH(1,1) to get the predicted price. However, I didnt understand variance that he calculates from the table. WHat is the formula?

A simple ARMA(1,0)-GARCH(1,1) model can be written as : $$y_t=\mu + \phi y_{t-1}+e_t$$ $$e_t \sim N(0, \sigma^2_t)$$ $$\sigma_t^2=\gamma + \beta e_{t-1}^2+ \eta\sigma_{t-1}^2$$
After calibrating the above model, you can use the first equation to forecast one day ahead exchange rate(expected exchange rate). For example: $$\mathbb{E}(y_t|\mathscr{F_{t-1}})=\mu_t+\phi y_{t-1}$$
Similarly, using last equation you can get conditional standard deviation. To get unconditional variance take expectation one more time:$$\mathbb{E[\sigma_t^2|\mathscr{F}_{t-1}}]=\gamma + \beta \, \mathbb{E}[e^2_{t-1}]+\eta \,\mathbb{E}[\sigma^2_{t-1}]$$ solving above equation, you will get $$\sigma_t^2=\frac{\gamma}{1-\beta -\eta}$$