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5. Suppose that GARCH(1,1) parameters have been estimated as o = 0.000003, a = 0.04,...

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5. Suppose that GARCH(1,1) parameters have been estimated as o = 0.000003, a = 0.04, and = 0.94. The current daily volatility is estimated to be 1%. Estimate the daily volatility in 30 days. 6. Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility estimate using (a) The EWMA model with = 0.94 (b) The GARCH(1,1) model with o = 0.000002, a = 0.04, and = 0.94. 7. Suppose that the parameters in a GARCH(1,1) model are a = 0.03, b=0.95 and w= 0.000002. (a) What is the long-run average volatility? (b) If the current volatility is 1.5% per day, what is your estimate of the volatility in 20, 40, and 60 days? (c) What volatility should be used to price 20-, 40-, and 60-day options? (d) Suppose that there is an event that increases the volatility from 1.5% per day to 2% per day. Estimate the effect on the volatility in 20, 40, and 60 days. (e) Estimate by how much the event increases the volatilities used to price 20-, 40-, and 60-day options. 8. What does covariance measure and how is it estimated

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