Category Archives: Extreme Value

Looking for extremely rare events ?

As mentioned in a recent post on (here), David Viniar who used to work as a director for Goldman Sachs mentioned that « We are seeing things that were 25-standard deviation events, several days in a row », (seehere). It was in 2007 much before the recent financial crisis (and the recent – real – extremal events)
I have to confess that I couldn’t do the maths with R, but this has been done recently in a research paper,
Dowd, K.; Cotter, J.; Humphrey, C.; Woods, M.(2008), « How unlucky is 25 sigma? », Journal of Portfolio Management, Vol.34(4), pp.76-80
It turns out that 25 times the standard deviation, for a gaussian distribution, is as unlikely yo happened as winning 21 or 22 consecutive weeks at the BritishNational Lottery ! So who can still believe that Gaussian distributions can still be used in financial econometrics ?

Statistical seminar at Belo Horizonte

Talk at the statistical seminar at the university of Belo Horizonte, Wednesday, onmultivariate extremes. Slides can be downloaded here.

The talk will give a detailed introduction on multivariate extremes and related concepts. Then the case of Archimedean copula will be fully described (following the paper with Johan Segers).

Many thanks to Renato Martins Assunção (here) for inviting me for a couple of days in Belo Horizonte ! Thanks also for your interest in my blog… and since I understood that some people who do not speak French might be interested in my blog, I started to write my blog in English (or at least a langage that should not be too far away from English). There is a nice discussion about langage on this blog (here, unfortunately in French…)

Copulas, risk dependence and applications to Solvency II

Exposé dans le cadre de la Summer School of the Groupe Consultatif Actuariel Européen: Enterprise Risk Management (ERM) and Solvency II. Petite réflexion à partir des déclarations du rapport technique QIS3, en particulier la déclaration qui mériterait des heures de commentaires,
In view of the insufficiency of currently available data, the setting of these correlation coefficients will necessarily include a certain degree of judgement. This is also true because, when selecting correlation coefficients, allowance should be made for non-linear tail correlation, which is not captured under a “pure” linear correlation approach. To allow for this, the correlations used should be higher than simple analysis of relevant data would indicate.