GARCH and Volatility Estimation in Expected Shortfall Models

# Is GARCH (and or it's variations) actually used in risk-modelling for expected-shortfall?


# Is GARCH (and or it's variations) actually used in risk-modelling for expected-shortfall?












I understand there are limitations and practicality issues with GARCH, but does any company actually use it in their risk-management system when calculating their expected-shortfalls? Even as a basis with other components layered on, and extra estimation, tinkering etc?

If it is, is there actually any evidence of this with someone who's written a book/paper who's previously worked in a risk-management department at an financial institution? Every practitioner's guide I find is written by career professors.

## Answer by Dimitri Vulis (score 3, accepted)

https://quant.stackexchange.com/a/81364

I found an example: Martin Auer. Hands-On Value-at-Risk and Expected Shortfall: A Practical Primer. Springer (2018). The blurb gives his affiliation as Raiffeisen Bank International, Vienna, Austria. (note: I condemn Raiffeisen for doing business in Russia.) His linkedin profile also mentions Bank of America. We can assume that whatever he describes is close to what some large and medium banks actually use. He writes (page 46):

> Location of Local Vola Window The time series of returns exhibit varying vola levels, also called heteroscedasticity. A vola rescaling operator does not leverage but actively tries to destroy this property. To do this, it must estimate the local volatility of the region a return resides in.

> The textbook approach for this is to use so-called GARCH (short for, you guessed it, generalized autoregressive conditional heteroscedasticity) models. Such models are mathematically sound and widely used in literature. In fact, the original filtered historical VaR simulations rely on GARCH, which makes its application easy to defend. (Footnote: Just as nobody got ever fired for buying IBM, no vola model was ever rejected for relying on GARCH.) But GARCH models must be fit first—in our case, 2200 times or once for each risk factor, and repeatedly. This means an increased implementation effort and plenty of things that can go wrong. It also makes it difficult or impossible to precisely reenact model results for anyone who does not command a ready time series analysis kit. For these reasons, we propose to use a poor man’s version of a vola estimate, the plain standard deviation.

> When using the standard deviation, it is tempting to stick with as many GARCH conventions as possible to minimize any perception of deviation from an ingrained, established method. Since GARCH is essentially a regression-based approach, it relies on returns up to, but not including, the day for which a vola is estimated. In that line, the standard deviation of those same, preceding returns could be used for estimating the local vola of a return about to be rescaled. This is not necessary, however, as the standard deviation is simply not bound by regression limitations. In fact, if you were tasked to come up with a risk factor’s volatility for some January 15, you would most likely take the standard deviation of that month’s returns, never even considering to drop the return of the 15th itself from that estimate...