Back testing Expected Shortfall

Hello everyone,

I work at a university in 
germany and we are also currently working on forecasting ES and (of 
course) backtesting of said forecasts.

Over the last few months some students, who are writing their masters
thesis at our chair, had to some litarature research.
Thats why I wanted to give you a very brief overview of their findings:

The
 most widely applied ES backtests seems to be the backtest by McNeil, 
Frey and Embrechts (2000), implemented for example in the rugarch 
package.
(the test was already mentioned here by Alexios)

In addition to the already mentioned tests and the paper by Acerby and
Szekely I wanted to add the following:

A
 Hitsequence based backtest was introduced for by Du, Escanciano (2017).
 As far as I am concerned, this test has not yet been implemented in a 
package, but their code is available online. In a broader view, this 
test is a special case of a spectral measure test by Costanzino, Curran 
(2014), which was then extended to a Basel-Like traffic light approach 
in 2018 (Not sure about the availability of code).

In
 Emmer et al. (2015) it is suggested, that a suitable ES forecast can be
 approximated by only 4 different VaR forecasts. This also suggests, 
that you can backtest ES, forecasted by a model that forecasts both, ES 
and VaR, such as GARCH, by backtesting th 4 different VaR forecasts.
However this approach seems to need more empirical valuation.

I
 also wanted to mention the paper by Gneiting (2011), showing that the 
ES lacks elicitability property. This can lead to complications, when 
you try to backtest the ES itself as a point forecast.However, this 
property can be used to construct a model comparison like backtest as in
 Fissler et al. (2015).

More reacently, a 
quantile regression based approach has been suggested by Coupier, 
Leymarie (2020). I have not yet read said paper and therefore I can not 
tell you anything about it.

I hope that this message gives you some new insights and some usefull
information.

Best regards,
Pit

Research Associate
Martin-Luther-Universit?t Halle-Wittenberg
Chair of Finance & Banking

Gro?e Steinstra?e 73 | D-06108 Halle | Germany
Tel 0049 345 5523452

Back testing Expected Shortfall

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