Risk Analysis
J.-F. Delmas (ENPC), P. Tankov

Location: Amphi Caquot, ENPC, rue des St Pères, Paris 5ème.

Schedule: wednesday morning (8h30-12h).

Days (Theoretic foundations) (2007): 17/10, 7/11, 14/11, 28/11, 5/12, 12/12, Exam 19/12 (location: TBA).

¥ Aims

Following "Basel Committee on Banking Supervision", risk analysis is now a major issue for the Bank community. In this lecture, we present in a first part the theoretical foundation on risk measures in finance: monetary measures of risk, Value at Risk, Conditional Value at Risk, High quantile estimation, Extreme value theory, Dependance, Copulas. The second part of the lecture is devoted to the computation and use of risk measures in the Banking community.

Program (Theoretical foundations): Jean-François Delmas (Ecole Nationale des Ponts et Chaussées) and Valdo Durrleman (Ecole Polytechnique).

-- Lect. 1. Introduction: Basel recommendation, use of the value at risk. Monetary, convex, coherent risk measures (I).

-- Lect. 2. Monetary risk measures; property of the VaR and CVaR (II).

-- Lect. 3. Quantiles: definitions and estimation using extreme value theory (I).

-- Lect. 4. Quantiles: estimation using extreme value theory (II).

-- Lect. 5. Correlation modelisation using copulas.

-- Lect. 6. Simulation, estimation for copulas.

-- Exam (3h). Authorized documentation: one page of handwritten notes. Previous Exams: 2006 (pdf).

¥ Bibliography

-- Basel Committee on Banking Supervision. International convergence of capital measurement and capital standards.

-- H. Fšllmer and A. Schied. Stochastic finance. An introduction in discrete time. Volume 27 of de Gruyter Studies in Mathematics. 2004.

-- A. J. McNeil, R. Frey, and P. Embrechts. Quantitative risk management. Concepts, techniques and tools. Princeton Series in Finance. 2005.

-- T. Roncalli. La gestion des risques financiers. Economica. 2004.

¥ Other bibliography

-- J. Beirlant, Y. Goegebeur, J. Teugels, and J. Segers. Statistics of extremes. John Wiley & Sons Ltd. 2004.

-- P. Embrechts, C. Klueppelberg, and T. Mikosch. Modelling extremal events for insurance and finance. Volume 33 de Applications of Mathematics, Springer. 1997.

-- R. B. Nelsen. An introduction to copulas. Volume 139 de Lecture Notes in Statistics, Springer. 1999.

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