Tail events

There are two ways to measure VaR (Value at Risk):

• Finding quantiles using empirical data
• Matching a parametric distribution to data

ETL (Expected Tail Loss) takes averages of the tail value at risk to provide better perspective for tail risk outcomes.

There are still drawbacks to using empirical data.

"The most powerful statistical techniques cannot make short histories reveal once-in-a-lifetime events." (Jorion, Chapter 5)

For this, we move on to Stress Testing.