# No more tasty surprises: Calculating the probability of extreme events

##### September 26, 2011

It had to happen: the property bubble burst and the global financial market experienced its biggest crisis in the last hundred years. In retrospect, many suspected it was coming, but nobody could have known for sure. The traditional investment strategy failed, as all forms of investment suddenly collapsed at the same time. In order to calculate the probability of several such extreme events occurring at the same time, three scientists at the RUB have developed a new method. Prof. Dr. Holger Dette, Dr. Axel Bücher und Dr. Stanislav Volgushev from the Institute of Statistics (Faculty of Mathematics at the Ruhr-Universität) published their findings in the prestigious scientific journal "The Annals of Statistics".

Big things start small

Up to now, when statisticians estimated the probabilities of , they usually calculated with dependencies between the outliers of statistical series. The outliers, however, make up the smallest part of a data set, e.g. the largest 100 out of 3,600 data. That means they ignore the dependencies of the bulk of the relevant data set, namely 3,500 data, and thus take the risk that important information is lost. Axel Bücher shows how this problem can be solved: "Our work provides a decision aid as to whether it is better to use the full range of data and not only the outliers. If all the data are relevant, then they should all be included. However, this is not always the case. Sometimes these data would falsify the result."

Multidimensional function

The researchers use the copula function for the evaluation. "This is a complicated, multi-dimensional function, which characterises stochastic dependencies between the data" explains Stanislav Volgushev. With this aid, a few years ago we might have noticed that many little termites were nibbling their way into the wooden foundation of the global financial market, whilst we were on the look out for large predators.

Financial crises as motivation for research

"Our research is strongly motivated by the recent financial crises. At that time, almost all the economic models and forecasting tools for loan losses failed because they did not pay sufficient attention to extreme dependencies. In the long run, we aim to develop models and methods that predict such events better" says Prof. Dette, explaining the reason for their research. For several years, the three researchers have been looking into new methods of asymptotic statistics which work with sample sizes approaching infinity. They are financed by the German Research Foundation (DFG) in the Collaborative Research Centre SFB 823 "Statistical modelling of nonlinear dynamic processes". The English-language publication bears the title "New estimators of the Pickands dependence function and a test for extreme-value dependence".

More information: Axel Bücher, Holger Dette, Stanislav Volgushev: "New estimators of the Pickands dependence function and a test for extreme-value dependence", in: "The Annals of Statistics", Volume 39, Number 4, 2011. doi: 10.1214/11-AOS890 http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.aos/1314190620&page=record

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##### Shelgeyr
5 / 5 (2) Sep 26, 2011
Is "Tasty" in the headline a typo? It seems they probably meant "Nasty", but with the metaphore of termites "nibbling their way into the wooden foundation of the global financial market", it is hard to be certain.

Just curious...
##### Nanobanano
not rated yet Sep 26, 2011
Any market system designed to concentrate wealth in the hands of the already wealthy plus a few speculators and a few executives is doomed to fail one way or another.

History shows repeatedly that this whole "aristocracy takes everything" cycle always leads to a collapse, in some cases even revolutions.

What does every depression have in common with the American Revolution and the French Revolution? For starters, the wealthy attempt to gobble up everything and the system collapses when ordinary people cannot bear the burdens demanded by their task masters any more.

Too many things in our economy are just a ripoff designed to funnel money into the hands of the very rich, or into the hands of middlemen due to ridiculous licensing regulations, an example of this is the recent trend of the owner of a contracting company in home construction makes more money in PERSONAL profits than most of the labor costs of the entire project.
##### Nanobanano
5 / 5 (2) Sep 26, 2011
Anywhere from 10% to 25% of the cost of a new home (or a small apartment building) is the PERSONAL INCOME of the contractor, while the sub-contractors and laborers who actually build a home often barely make a net income on a project by the time you figure cost of tools and gasoline to drive to work, and of course, work clothes which typically get destroyed quite quickly in residential construction.

Anyway, sorry for the digression. I'm making the point that the middlemen and CEO things in this country are hurting us at every level of our civilization by increasing costs unnecessarily.
##### Shelgeyr
not rated yet Sep 26, 2011
@Nanobanano said:
I'm making the point that the middlemen and CEO things in this country are hurting us at every level of our civilization by increasing costs unnecessarily.

By "this country" I assume you mean the USA (and my apologies if you don't). If so, I have to disagree.

Those "middlemen and CEO things" who engage in "crony capitalism" or outright criminal behavior, hurt us at every level, but criminals and "crony capitalists" (who, for the record, aren't really Capitalists at all, which is why they resort to cronyism - i.e. they can't hack it in the market otherwise) have always hurt us and always will, whether they're middlemen, CEOs, or whatever.

Currently, I think you'd make a much better point if you'd said "The Federal Government, and those of many States, are hurting us at every level... by increasing costs unnecessarily", which is not only a true (IMHO) statement, but should be followed up with tar and feathers, or pitchforks and torches. Whichever.