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Suppose that the parameters in a GARCH ( 1 , 1 ) model are = 0 . 0 3 , = 0 . 9 5

Suppose that the parameters in a GARCH (1,1) model are =0.03,=0.95 and =
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? Hint: use =
(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.Suppose that the parameters in a GARCH(1,1) model are \alpha =0.03,\beta =0.95 and \omega =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? Hint: use \alpha = ln(1/0.98
(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.
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