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?

(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.

AppendixLO1