Suppose that the parameters in a GARCH(1,1) model are a = 0.03, fi = 0.95, and co = 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 current volatility by 0.5% to 2% per day.

Estimate the effect on the volatility in 20, 40, and 60 days.

e. By how much does the event increase the volatilities used to price 20-, 40-, and 60-day options?