Suppose that you are presented with 2 models: (i) an EWMA model with parameter =0.91; and (ii) a GARCH (1,1) model with parameters =0.09,=0.90, and = 0.000008 a) What is the long-run average volatility in both models? [4 marks] b) Assume that the most recent retum un-1 is estimated at 2% and the most recent volatility n1 is estimated at 1%. Update the volatility estimate in both models. [4 marks] For all the remaining items, consider only the GARCH (1,1) model: c) If the current volatility is 0.5% per day, what is your estimate of the volatility in 5 , 100 , and 500 days. [4 marks] d) What volatility should be used to price 5-, 100-, and 500-day options? [4 marks] e) Suppose that there is an event that increases the volatility from 0.5% per day to 1.5% per day. Estimate the effect on the volatility in 5,100 , and 500 days. [4 marks] f) Estimate by how much the event increases the volatilities used to price 5-, 100 -. and 500-day options