Use the AIC and autocorrelation tests to find an adequate ARMA- GARCH specification for the log returns.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. (5 points) Volatility Modeling

1. Load the EUROSTOXX50 dataset as a modern time series object into your working environment and plot it.

2. Use the AIC and autocorrelation tests to find an adequate ARMA- GARCH specification for the log returns. Consider normal as well as t-distributed residuals.

3. Does your result support the premise of volatility clustering?

4. Use a GJR-GARCH(1,1) model to check whether leverage effects are present in the data.

5. Use an EGARCH(1,1) for the same purpose. What can be inferred?

2. (5 points) Downside Risk Modeling

1. Compute and plot the empirical distribution function of the EUROSTOXX50 log- returns.

2. What is the whole-sample empirical VaR and ES at the 99% level?

3. Compute time-varying estimates of VaR (99%) and ES (99%) with Historical Simu- lation. Use data from the previous 250 trading days in each period.

4. Plot the log-returns together with the computed VaR and ES series in a time series graph.

5. Backtest your VaR estimates for violation independence as well as correct conditional and unconditional coverage.

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