Asset A at the close of trading yesterday was $$102,$ and the daily volatility was estimated

to be $1\%$ per day today. Suppose the price at the close of trading today is $$107.$

a$.$ What is the log$-$return today?

b$.$ Consider the RiskMetrics model with $=0\mathrm{.}94.$ What is the new volatility tomorrow?

c$.$ Consider the RiskMetrics model above. What is the ten$-$day ahead $1\%$ VaR?

d$.$ Consider the GARCH $(1,1)$ model with $=0\mathrm{.}000005,=0\mathrm{.}05,$ and $=0\mathrm{.}90.$

What is the new volatility tomorrow?

e$.$ Consider the GARCH $(1,1)$ model above. What is ten$-$day ahead $1\%$ VaR?