Risk measures and extremes

N. Alfonsi - L. Abbas-Turki

This course takes place from October to December - 6 sessions of 3 hours per week.

Organisation in the course website: http://cermics.enpc.fr/~alfonsi/mrf.html

The aim of this course is to present the tools for risk measurement concerning the trading room and the management of the “book” (portfolio of assets) for a short time scale (1 to 10 days). The main theoretical topics will be: extreme value theory, multidimensional risk representation via copulas, monetary risk measures and their various interpretations as well as the presentation by market participants of their practical implementation, regulatory standards concerning short-term market risk, VaR and its implementation, model risk management and reserve calculation on derivative books.

This ECUE of the “Finance” EU constitutes the theoretical part of a course offered within the framework of the “Financial Risk Chair” of the Risk Foundation, a partnership between École Polytechnique, École des Ponts ParisTech and Société Générale. This year, it is taught in cooperation by a teacher from the Pierre and Marie Curie University and a teacher from the Ecole des Ponts ParisTech.

  • Introduction: the framework of the Basel recommendations, measuring risk with value at risk. Monetary, convex, consistent risk measures (I).
  • Monetary risk measures: properties of VaR and CVaR (II).
  • Exiting the Gaussian model to calculate VaR. Quantiles: definitions and estimation using the extreme value law theory (I).
  • Quantiles: estimation using extreme value law theory (II).
  • Modelling correlations: copulas.
  • Simulation, estimation of copulas.
  • Knowledge control (3h).


  • J. Beirlant, Y. Goegebeur, J. Teugels, and J. Segers. Statistics of extremes.Wiley Series in Probability and Statistics. John Wiley & Sons Ltd., Chichester, 2004.
  • P. Embrechts, C. Klueppelberg, and T. Mikosch.Modelling extremal events for insurance and finance volume 33 of Applications of Mathematics, Springer, Berlin, 1997.
  • H. Föllmer and A.Schied.Stochastic finance, volume 27 of de Gruyter Studies in Mathematics Walter de Gruyter & Co., Berlin, extended edition, 2004. An introduction in discrete time.
  • A. J. McNeil, R. Frey, and P. Embrechts.Quantitative risk management Princeton Series in Finance. Princeton University Press, Princeton, NJ, 2005. Concepts, techniques and tools.
  • T. Roncalli. La gestion des risques financiers. Politique générale, Finance et Marketing. Economica, Paris, 2004. Collection Gestion.