1. Wrap-up
Congratulations, you have reached the end of the course. However, that's not to say it is the end of the story.
2. Not the end of the story...
While the methods you have looked at in this chapter are, in fact realistic, and known to be used in practice, it is definitely possible to improve on them.
A couple of enhancements are worth mentioning.
The information about serial dependence wasn't explicitly used in the risk calculations in chapter 4. It is possible to improve the risk sensitivity of the VaR and expected shortfall estimates by using some of the information about volatility clustering in the return series.
This can be achieved by a method known in industry as filtered historical simulation. The intuition is that the VaR and ES estimates are scaled by a measure of the predicted volatility for the risk horizon in question.
In other words, if recent data indicate that the volatility is likely to be high, a higher scaling is applied to the VaR or ES estimate. If recent data indicate that the volatility is likely to be low, a lower scaling is applied to the estimates.
In order to model changing volatility and make volatility predictions, more time-series techniques are required, in particular ideas like GARCH models and exponentially-weighted moving average (or EWMA) volatility filters.
The other issue I wanted to briefly mention is the fact that the simple empirical estimators of VaR and expected shortfall used in the exercises are not the most efficient. They are subject to large errors, particularly when the sample sizes are modest.
The precision of the estimates can be improved by using parametric tail models for the historically simulated data. Relevant techniques here include heavy-tailed distributions and extreme value theory.
If you want to know more, you could consult my book "Quantitative Risk Management: Concepts, Techniques, and Tools".
3. Thanks for taking the course!
That's all from me. Thanks for taking the course, and good luck with managing your risks.