Suppose that you are presented with 2 models: (i) an EWMA model with parameter l=0.89; and (ii) a GARCH(1,1) model with parameters a= 0.09, b= 0.91, and w = 0.000008. a) What is the long-run average volatility in both models? [4 marks] b) Assume that the most recent return un-1 is estimated at 1% and the most recent volatility sn-1 is estimated at 2%. Update the volatility estimate in both models. [4 marks] For all the remaining items, consider only the following GARCH(1,1) model with parameters a= 0.08, b= 0.91, and w = 0.000005. c) If the current volatility is 1.5% per day, what is your estimate of the volatility in 50, 75, and 800 days. [4 marks] d) What volatility should be used to price 50-, 75-, and 800-day options? [4 marks] e) Suppose that there is an event that decreases the volatility from 1.5% per day to 0.5% per day. Estimate the effect on the volatility in 50, 75, and 800 days. [4 marks] f) Estimate by how much the event increases the volatilities used to price 50-, 75-, and 800-day options. [5 marks]