Yesterday the DowJones - and with them, the rest of the world’s Bourses - plunged because GE had worse results for this quarter than expected. We clearly see the tail wagging the dog, and all this because the financial world is so jittery.

How can this nervous state can be described mathematically ?
No doubt, volatility, as an outstanding parameter of the market’s underlying brownian, jumps into mind. But not only ! Maybe it was the volatility structure’s stochastic volatility itself that plays the dominant role.
Or, it is the Poisson jumps that changed frequency ?

There should be a few more other things. A sensitivity factor that reacts to trigger, Dirac events. Parameters that generates not only wider, but also, more frequent jumps. An increase in correlation that causes falls to give birth to more falls, and upswing modes to boost beyond reason upward trends.

In short, we should endeavour to put some parts of behavioural finance into equations…

Copulae are becoming more and more popular these days.

At least, let us say that there are more and more people who know that these strange contraptions are used to model risks. Not a lot of them though, would feel at ease calculating the compounded, “global” risk of a bank using copulae. Even less wouyld know how to compute the VAR (value at risk) of a copula.

Clearly the rogue trader at SocGen did not just overshoot his trading limits, and thus qualify for Basel Op Risk category 6 “Execution Delivery and Process Management” risk. He also usurpated his fellow traders identity, thereby causing Category 1:”Internal Fraud” risk exposure. And he hacked into Middle and Back Office servers, using what is nicely dubbed “social engineering”, creating breaches in Workplace security (category 3). We are looking here at an aggregated, correlated risk. A case for copula.

In order for each of these separate categories of risk to hatch a 99.9% tail event, one must wait for a long, long time - indeed, as a risk manager from Fortis once told me at the Committee of European Bank Supervisor 3 years ago, it’s Star Trek lifespans. But, when compounded, the global risk being calculated as a copula on these marginal individual risks, probabilities rapidly arrive at astounding levels easily. Properties of Copulae force the Iso-Value-at-risk hypersurface to be concave, and thus, each individual risk is less rare than what is expected from its frequency if it were alone.

Our different Projet de Fin d’Etudes on copulae have been the topic of studies and programming for 4 groups of 6 students each on the average, at ECE. Mortgage Credit risk and Operational risk have been studied through copulae. C++ and C# programs have been compiled into DLL’s called by Excel. You guys have all sweated through January and you have all loved them, be they called Franck’s or Student’s, be they Archimedean or just plain Normal.

A new way to view risk and chance, hazard and mishap, a little less qualitatively, a little more quantitatively. Thanks for your burning the midnight oil, guys ! Well done !

La gestion du risque (risk management), est une discipline qui connait un fort essor depuis plusieurs années. Loin de se limiter au domaine financier, elle peut s’appliquer pour toute organisation et activité.

Le Cadre de Référence de la Gestion des Risques est l’oeuvre d’un groupe de travail composé des principaux organismes de la
gestion des risques au Royaume Uni : l’Institute of Risk Management (IRM), l’Association of Insurance and Risk Managers (AIRMIC) et le National Forum for Risk Management in the Public Sector (ALARM).

Paru en 2002, il a pour objectif de préciser, au niveau du risk management pour une organisation :

• la terminologie,
• le processus de déploiement de la gestion,
• des risques,
• l’organisation de la gestion des risques,
• l’objectif de la gestion des risques.

http://www.theirm.org/publications/PUstandard.html

Traduction française : http://www.theirm.org/…/French_Risk_Management_Standard_021203.pdf