The most recent estimate of the daily volatility of an asset is 1.5% and the price of the asset at the close of trading yesterday was $30.00. The parameter λ in the EWMA model is 0.94.

Suppose that the price of the asset at the close of trading today is $30.50. How will this cause the volatility to be updated by the EWMA model?

5.l0. A company uses an EWMA model for forecasting volatility. It decides to change the parameter λ from 0.95 to 0.85.

Explain the likely impact on the forecasts.

5.l1. Assume that S&P 500 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 ω =0.000002, α = 0.06, and B = 0.92.

If the level of the index at close of trading today is 1,060, what is the new volatility estimate?