[R-SIG-Finance] Back testing Expected Shortfall

[Brian G. Peterson]

On Wed, 2020-06-10 at 15:08 +0530, Christofer Bogaso wrote:
> I was looking for an idea how banks backtest their models for
> Expected
> Shortfall. Backtesting VaR is well documented but I failed to get any
> practical idea about backtesting ES.
> 
> Any pointer towards the best practice will be really helpful.

If you are using Normal VaR, then you know the Expected Shortfall
estimate too.

If you are using a different mechanism, then of course the mean loss
when the loss exceeds the VaR may be significantly different than the
Normal ES.

So, to backetesting...  the newest Basel standard replaces VaR with ES,
and requires that banks justify their use of a particular ES model that
they are using to calculate required regulatory capital.

To the best of my knowledge, the most widely used and cited approaches
are outlined here:

https://dlu-umich.github.io/docs/Research_Insight_Backtesting_Expected_Shortfall_December_2014.pdf

Generally, I like the overall methodology presented by this paper.  The
only complexity is the need to store (or be able to recalculate) the
full distribution of the tail.  I don't see this as a giant roadblock,
since the tail distribution contains additional information of interest
anyway, the shape of the tail is useful in model validation and
fitting, and disk is cheap.

The models presented in the reference above, while not to my knowledge
directly implemented in R, should be able to be constructed from data
in the recent R packages by Ardia et. al. GAS:

https://journal.r-project.org/archive/2018/RJ-2018-064/RJ-2018-064.pdf

and MSGARCH:

https://www.sciencedirect.com/science/article/pii/S0169207018300840

Regards,

Brian


-- 
Brian G. Peterson
ph: +1.773.459.4973
im: bgpbraverock