EVT

[frm_daniel]

Hi David,

I got some questions on EVT which I don't know if my understanding is correct or not.
EVT application to VaR on stock market data is not useful. The reason is stock price is lognormal distributed and for empirical stock market data, standard VaR estimates at the 95% confidence level can be fairly accurate, and would not be benefit from the use of extreme value theory.

Also EVT can help avoid the shortcoming of the historical simulation method due to lack of data in the tails Does it correct ?
If there is not enought data in the tail, how could EVT "create" data in the tail?

Daniel

 

[David Harper CFA FRM]

Hi Daniel,

I could agree with the first but can we parse it:

* As question correctly suggests, EVT is compatible with VaR; e.g., Dowd's illustrations here of EVT-VaR:
http://www.bionicturtle.com/premium/spreadsheet/5.d.3._dowd_evt/

* In a nutshell, EVT is just giving us a parametric (i.e., function/analytical, NOT empirical) method to "zoom-in" on the tail of the distribution (child tail of the overall parent)

* Re: "stock price is lognormal distributed" is imprecise. Rather, our basic (introductory) MODEL (GBM) assumes lognormal price (normal log returns) for its sheer analytical convenience. We know that actual, empirical returns are non-normal. As actual, empirical (log) returns are non-normal, price must also not be lognormal. (and, think of Hull's chapter of the volatility smile/smirk: the volatility smile is a reflection of empirical reality, and its very existence proves empirical prices are not lognormal! We use a lognormal model in defiance of proof than empirical prices are not lognormal)

* This statement is very agreeable to the FRM: "standard VaR estimates at the 95% confidence level can be fairly accurate, and would not be benefit from the use of extreme value theory." Put another way, tail estimation is inherently imprecise; 95% is only a rough approximation. 99% even less so. EVT operating at 99.9% or 99.99% gives the illustration of false precision.

* But, okay, the counter argument is: if we use the lognormal (or other parent distribution) we will understate the fat tails. EVT is a means (not perfect, but maybe the best of all bad options) to fit a heavy-tail distribution when (i) we lack data for an empirical distribution and/or (ii) we deliberately want to calibrate a heavy-tail

Re: "Also EVT can help avoid the shortcoming of the historical simulation method due to lack of data in the tails "
Yes, think of the DB LDA case study, although it applies to operational data. They lacked empirical data (incl external) for op losses > $50 million, so they had no alternative bu to "graft" (piecewise) a parametric EVT distribution onto the tail. No data forced EVT. How does it create data? In the same way a normal distribution function "creates data" at every deviate (=NORMSDIST(z) = ?): with a smooth function line. We use a bit of date to calibrate the params, but then we are just using a function.

David