3. At the end of day on Black Monday (October 19th 1987), you would like to estimate the

term structure of VaRs and expected shortfalls on the S&P 500 index for the next 300 days.

The first thing you did is to fit a GARCH(1,1) model to the past two years of S&P return

data to obtain the one-step ahead volatility forecast (denoted by t+1), and the parameters

, , and of the GARCH(1,1) model.

Describe the steps you would take to estimate the term structure of VaRs and expected short-

falls using the Monte Carlo Simulation method, in which you use standard normal shocks

and you update future volatility using the GARCH(1,1) model. (17 points)