The level of difficulty of our course makes a little leap forward. Are you ready?
I am sure you are!
For the first time we enter into the statistical modeling of risk.

The topic of this week is Value-at-Risk, also known as VaR (sometimes also V@R).
The VaR is a fundamental tool in risk management. In the Basel framework, it plays a central role in all the main types of risk: market, credit and operational risk.

From a purely statistical point of view, Value-at-Risk is nothing more than a quantile of the loss distribution. However, in risk management, it represents one of the most important instruments for the determination of economic capital (and capital requirements).
Banks and financial institutions rely on VaR to determine the danger of potential losses.

During this week, we will introduce the VaR as a measure of risk, discussing its strengths and weaknesses. In particular, we will show that, generally speaking, Value-at-Risk is not a coherent measure of risk, and this may be a problem in terms of risk diversification.

Another measure of risk we will consider is the Expected Shortfall (ES). It will be clear that this measure is striclty related to VaR.
Later in the course (lecture 6), we will use both the VaR and the ES to actually determine the capital requirements of banks.

Finally, we will briefly discuss a statistical procedure we can use to test the reliability of the VaRs we compute. Its name is back-testing.
Since back-testing relies on the binomial distribution, if you are not familiar with it, please take some time to have a look.

This lecture contains:

Back to top