a)Suppose that = 0.94 and that yesterday's standard deviation of GM stock was 1%. During the day, the asset's return increased to 2%. Estimate today's volatility using the exponentially weighted moving average (EWMA) model.

b)Assume that the FTSE 100 at close of trading yesterday was 5,230 and the daily volatility of the index was estimated as 1.5% per day at that time. The estimated parameters in a GARCH(1,1) model are = 0.000002, = 0.06 and = 0.93. The level of the index at close of trading today is 5,140. Calculate the new volatility estimate.

c)Calculate and interpret the long-run volatility of the GARCH(1,1) model in (b).

d)The volatility of a stock price is 0.9% per day. Calculate the (approximate) annual stock price volatility.

e)A daily exponentially weighted moving average (EWMA) model with a decay factor of is used to develop a forecast of the (conditional) volatility. Which weight will be applied to the return that is three days old?