Instructions : ONLY DO $2.$ PART $($BUT MAKE SURE IT IS CORRECT AND COMPLETE AS REQUIRED$)$

Assume that the daily return of S&P $500$ index $(y_t)$ follows ARMA$(1,1)-$GARCH $(1,1)$ model as follows:

$y_t=c+a{y}_{t-1}+b{s}_{t-1}{e}_{t-1}+s_t{e}_t$

$s^2=a_0+a_l(s_{t-1}et-1{)}^2+b_1{s}_{t-1}^2$

$et$ iid $N(0,1)$

Read $2$ years S&P $500$ index $({?}^{GSPC})$ data from $09/15/2020$ to $09/15/2022.$

$1.$ Calculate $1-$day $99\%$VaR and i$.$e$.Va{R}_{1\%}(y_t)$ and $\{$:$CVa{R}_{1\%}(y_t)=AVa{R}_{1\%}(y_t)).$

$2.$Calculate $10-$day $99\%$ VaR and CVaR using Monte Carlo simulation method