1. What causes volatility? Explain the basic assumption and research supported view.

2. What does normal distribution mean and whether it applies to most of the market variables? Explain. 3. What assumption underlies the GARCH model in regard to volatility?

4. The volatility of an asset is 3% per day. What is the standard deviation of the percentage price change in 2 days?

5. Suppose that GARCH(1,1) parameters have been estimated as = 0.000003, = 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 l = 0.94 (b) The GARCH(1,1) model with = 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?