1.Assume that an index at close of trading yesterday was 1,040 and the daily volatility of the index was estimated as 1% per day at that time. The parameters in a GARCH(1,1) model are = 0.000002, = 0.06, and = 0.92. If the level of the index at close of trading today is 1,060, what is the new volatility estimate?

2.The parameters of a GARCH(1,1) model are estimated as = 0.000004, = 0.05, and = 0.92. What is the long-run average volatility and what is the equation describing the way that the variance rate reverts to its long-run average? If the current volatility is 20% per year, what is the expected volatility in 20 days?