Monday, April 16, 2012

Modelling Extremes

Modelling extreme events is a challenging business. By definition, you're dealing with observations that are way out there in the tail(s) of the distribution. But that's where a lot of exciting things happen!

I've played around a bit with extreme value theory (EVT) over the past four or five years, applying it to some interesting economic data. In 2009, Guang Bi and I  published a piece  that used EVT to analyse U.S. movie box office revenues (WP version here). It was a lot of fun!

Subsequently, Feng Ren and I published a piece (WP version here) that was a bit more "traditional . We applied EVT to the daily returns associated with crude oil prices.

Last month another paper co-authored with Qian Chen and Hui Feng, using EVT, appeared in Applied Financial Economics.  (WP version here.) As our abstract says:

"This article contributes to the literature in two respects by analysing an interesting international financial data set. First, we apply conditional EVT to examine the Value at Risk (VaR) and the Expected Shortfall (ES) for the Chinese and several representative international stock market indices: Hang Seng (Hong Kong), TSEC (Taiwan), Nikkei 225 (Japan), Kospi (Korea), BSE (India), STI (Singapore), S&P 500 (US), SPTSE (Canada), IPC (Mexico), CAC 40 (France), DAX 30 (Germany), FTSE100 (UK) index. We find that China has the highest VaR and ES for negative daily stock returns. Second, we examine the extreme dependence between these stock markets, and we find that the Chinese market is asymptotically independent of the other stock markets considered".
There are lots of really interesting applications of EVT with economic and financial data, just waiting to be taken up. If you get interested in this field, then you'll find some great R packages to help you see here. Ones that I've found helpful include the POT package (Ribatet, 2007), and the evd package (Stephenson, 2008).

However, do be careful. It's well known that there are some really big challenges when it comes to ML estimation of the underlying distributions, such as the Generalized Pareto distribution. More on this in a forthcoming post.



References

Bi, G. and D. E. A. Giles, 2009. Modelling the financial risk associated with U.S. movie box office earnings. Mathematics and Computers in Simulation, 79, 2759-2766.

Chen, Q., D. E. Giles and H. Feng, 2012. The extreme-value dependence between the Chinese and other international stock markets. Applied Financial Economics, 22, 1147-1160.

Ren, F. and D. E. Giles, 2010. Extreme value analysis of Canadian daily crude oil prices. Applied Financial Economics, 20, 941-954.

Ribatet, M. A., 2007. A user’s guide to the POT package, version 1.4.

Stephenson, A., 2012. evd: Functions for extreme value distributions. http://cran.r-project.org/web/packages/evd/evd.pdf



© 2012, David E. Giles

2 comments:

  1. My only problem with the Generalized Pareto distribution is that from a portfolio management prospective it becomes more difficult to optimize when you're dealing with securities with infinite variance.

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  2. It was very interesting research! Looking forward to working with you again, David!

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