Chaire Risques Financiers

Updated: 21/01/2010 12:01

Chaire Risques Financiers

Les travaux de cette chaire sont conduits principalement par des équipes de l'Ecole Polytechnique et de l'Ecole Nationale des Ponts et Chaussées. Elle bénéfécie d'un partenariat avec la Société Générale .
Cette chaire est coordonnée par la Fondation du Risque .

Thèmes de recherche

- L'amélioration des méthodes numériques utilisées par les Institutions financières (Monte-Carlo notamment)
- Développement de modèles en grande dimension, basés sur la théorie des matrices aléatoires
- L'étude des moyens de prévention et de maîtrise des risques, en prenant en compte les problèmes de liquidité dans la couverture dynamique et la volatilité
- Création de nouveaux outils consacrés à l'arbitrage statistique, au pricing de dérivés complexes, et à la recherche sur les dérivés de crédit

During the year 2009, the research activity of the chair was structured around three main topics:
risk measurement and management, numerical methods, Statistics of finance.

Membres de la chaire

Nicole EL-KAROUI (responsable Scientifique)

ENPC:
• A. Alfonsi, Chercheur à l'Ecole des Ponts
• J.-F. Delmas, Chercheur à l'Ecole des Ponts, Professeur Chargé de cours
à l'Ecole Polytechnique
• B. Jourdain, Professeur à l'Ecole des Ponts, Professeur Chargé de cours à l'Ecole Polytechnique
• B. Lapeyre, Professeur à l'Ecole des Ponts,

Polytechnique:
• Emmanuel Bacry, Chercheur CNRS à l'Ecole Polytechnique
• Nicole EL KAROUI , Chercheur à l'Ecole Polytechnique, Professeur à l'Université
Paris VI
• Alfred GALICHON , Professeur chargé de cours à l'Ecole Polytechnique (Departement
Economie)
• Caroline HILLAIRET , Maître des Conférences à l'Ecole Polytechnique
• Mathieu ROSENBAUM , Professeur chargé de cours à l'Ecole Polytechnique
• Peter TANKOV , Professeur chargé de cours à l'Ecole Polytechnique
• Nizar TOUZI , Professeur à l'Ecole Polytechnique.

Evénements

1- Mars 2008 : forum « Risque de Crédit » du Pôle de Compétitivité (participation à l'organisation)
2- Mai 2008 : Workshop à Paris sur les nouveaux développements en Finance de marché (avec Columbia-U et Florida U). 100 inscrits, 60 présents
3- 22 mai 2008 : Workshop en l'honneur de B. Dupire
4- Septembre 2008 : Participation à l'Ecole d'Eté Européenne à Dourdan. 150 candidats, dont 50 retenus, ainsi que 65 doctorants

5- Third Conference on Numerical Methods in Finance, ENPC, 15-17 April 2009

This conference was organized by A. Alfonsi, J.-F. Delmas, B. Jourdain and B. Lapeyre with the help of the scientic committee headed by D. Talay and composed of H. Berestycki, J.Cvitanic, P. Garampon, G. Pages and C. Rogers. Over 140 participants were welcomed at Ecoledes Ponts during the 3 days of the conference. The plenary talks were given by:

- Yacine Ait Sahalia, PRINCETON UNIVERSITY : The Fine Characteristics of Jumps and Volatility in High Frequency Financial Data,
- Damiano Brigo, FITCH SOLUTIONS : Credit Derivatives pre- and in-crisis: Dynamical models implying armageddon scenarios and extreme losses,
- Rama CONT , CNRS & COLUMBIA UNIVERSITY : Too interconnected to fail: contagion and systemic risk financial networks,, National University of Singapore : Numerical Methods for Portfolio Selectionwith Transaction Costs,
- Pierre Henry-Labordere, Société Générale : Numerical Methods for Non-Linear Problems in Quantitative Finance,
-Arturo Kohatsu-Higa, University of Osaka : Approximations for SDE's driven by Levyprocesses.

Moreover, 46 talks were given in parallel sessions dedicated to Monte Carlo methods, variance reduction techniques, discretization of partial dierential equations, Stochastic differential equations and backward stochastic dierential equations, calibration of models, optimal stopping
and American options, tree methods, quantization,... The conference dinner organized at the Musee d'Orsay after a visit of the collections was appreciated by the participants.

6- Second SMAI European Summer School in Financial Mathematics, Paris, August 24{29, 2009 The second edition of the European summer school in nancial mathematics took place at the CRC Castle on HEC Campus (Jouy-en-Josas). All the information about the summer school is available at the web site:

http://www.cmap.polytechnique.fr/~euroschoolmathfi09/

This second edition of the summer school attracted 80 participants among which 60 PhD students.
The summer school was structured around two minicourses followed by short presentations given by PhD participants. One afternoon was dedicated to interaction with nancial institutions, with presentations by J. Lebuchoux (Reech AiM) and M. Simmonds (Nomura). The minicourses were:

-Financial modeling under illiquidity by P. Bank (Berlin) and A. Schied (Mannheim).
-Backward stochastic dierential equations with nancial applications by E. Gobet (Grenoble)
and J. Ma (Los Angeles).

The contributed talks by PhD participants were focused on a variety of topics including pricing, approximations of stochastic processes, mathematical theory of nance, xed income models, credit risk, illiquidity models, optimal investment, statistical methods. The Third edition of the summer school will take place in August 2010 at the same location.

Publications

Publications 2008

[1] Y. Jiao, N. El Karoui and D. Kurtz, "Valuation and VaR computation for CDOs using Stein's method", in Applied Quantitative Finance, 2nd Version (eds. W.Härdle, N. Hautsch and L. Overbeck), Springer 2008.
[2] Y. Jiao, N. El Karoui and D. Kurtz, "Gauss and Poisson approximations: application to CDOs pricing", Journal of Computational Finance, Vol.12, Winter 2008/09, pp.31-58
[3] Y. Jiao, N. El Karoui, "Stein's method and Zero-bias transformation for CDO tranches pricing", accepted to Finance and Stochastic s
[4] V. Durrleman - N. El Karoui, "Coupling smiles", Quantitative Finance, 2008,vol.8,issue 6,pp.573-590
[5] P.Barrieu - N. El Karoui, "Pricing, Hedging, and Designing Derivatives with Risk Measures", "Indifference Pricing: Theory and Applications, Edited by René Carmona (2008) Chapter 3, pp.77-141.
[6] N. El Karoui, S.Hamadène-A.Matoussi, "BSDEs and Applications", "Indifference Pricing: Theory and Applications, Book Edited by René Carmona (2008), pp.267-303
[7] C. Ravanelli and N. El Karoui "Cash Sub-additive Risk Measures under Interest Rate Ambiguity", to appear in Mathematical Finance
[8] A. Matoussi and S. Crépey , "Reected and doubly reected BSDEs with jumps: A priori estimates and comparison", Ann. Appl. Probab., vol. 18, N. 5 (2008), 2041-2069.
[9] U. Cetin, M. Soner et N. Touzi, Option hedging for small investors under liquidity costs, à paraître dans Finance and Stochastics.
[10] R. Elie et N. Touzi, Lifetime optimal consumption and investment under draw-down constraint, Finance and Stochastics 12, 3 (July 2008), pp. 299-330.
[11] A. Porchet, N. Touzi et X. Warin, Valuation of commodity power plants under investment and production constraints, Mathematical Methods of Operations Research, June 2008.
[12] R. Carmona et N. Touzi, Optimal Multiple Stopping and Valuation of Swing Option, Mathematical Finance 18, 2 (April 2008) pp. 239-268.
[13] E. Jouini, W. Schachermayer et N. Touzi, Optimal risk sharing under variant monetary utility functions, Mathematical Finance 18, 2 (2008), pp. 269-292.6
[14] G. Carlier, I. Ekeland et N. Touzi, Optimal derivatives design for meanvariance agents under adverse selection, Mathematics and Financial economic s 1, 1 (April 2007), pp. 57-80.
[15] I. Ben Tahar, M. Soner et N. Touzi, The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes, SIAM Journal on Control and Optimization 46, 5 (2007), pp. 1779-1801.
[16] M. Soner and N. Touzi, Hedging under gamma constraints by optimal stopping
and face-lifting. Mathematical Finance, 17, 1, 59-80 (2007).
[17] R. Elie, J.-D. Fermanian et N. Touzi, Kernel estimation of Greek weights by parameter randomization, The Annals of Applied Probability, 17, 4 (2007),1399-1423.

Pré-publications 2008

[18] B. Bouchard et N. Touzi, Weak dynamic programming principle for viscosity solutions.
[19] G.-E. Espinosa et N. Touzi, Detecting the maximum of a mean reverting scalar diffusion.
[20] A. Fahim et N. Touzi, A Numerical probabillistic schemes for fully nonlinear PDEs.
[21] D. Crisan, K. Monalorakis et N. Touzi, On the Monte Carlo simulation of
Backward SDES: an improvement on the Malliavin weights.
[22] M. Soner et N. Touzi, The dynamic programming equation for second order
stochastic target problems.
[23] R. Aïd, G. Chemla, A. Porchet et N. Touzi, On vertical integration in commodities markets.
[24] I. Ben Tahar, M. Soner et N. Touzi, Modelling continuous-time nancial markets with capital gains taxes.
[25] B. Bouchard, R. Elie, N. Touzi " Stochastic target problems with controlled loss "
[26] P. Tankov "Pricing and hedging gap risk"
[27] N. El Karoui, M. Jeanblanc, and Y. Jiao, "What happens after a default: a density approach"
[28] Y. Jiao, N. El Karoui and M. Jeanblanc, "Dynamic modelling of successive defaults
[29] L.Carasso, N. El Karoui and J.Obloj, " On the Bachelier Draw-Down equation and Azema-Yor martingale"
[30] A. Galichon and M. Henry, "Comonotonic measures of multivariate risks"
[31] A. Galichon and M. Henry, "Dual Theory of Choice under Multivariate Risks"
[32] A. Galichon, "The VaR at Risk".
[33] Mathieu ROSENBAUM , Volatility estimation under endogenous microstructure noise, with Christian Y. ROBER t (01/2009).
[34] Mathieu Rosenbaum, A new approach for the dynamics of ultra high frequency data: the model with uncertainty zones, with Christian Y. Robert (01/2009).
[35] M. Rosenbaum and C. Y. Robert, "Ultra high frequency volatility and covolatility estimation in a microstructure model with uncertainty zones" ENPC
[36] A. Alfonsi and B. Jourdain, "General Duality for Perpetual American Options", International Journal of Theoretical and Applied Finance, 11(6), pp. 545-566, 2008.
[37] B. Jourdain and A. Zanette, "A Moments and Strike Matching Binomial algorithm for Pricing American Put Options", Decisions in Economics and Finance 31, pp 33-49, 2008.
[38] J.Lelong, "Almost sure convergence of randomly truncated stochastic algorithms under veriable conditions", 2008, Statistics & Probability Letters

Publications 2009 (Polytechnique)

[1] R. Aid, L. Campi, A. Nguyen Huu et N. Touzi (2009). A Structural Risk Neutral Model of Electricity Prices, International Journal of Theoretical and Applied Finance.
[2] E.Bacry et J.F.Muzy (2009). Multifractal models for asset prices, To appear in Encyclopedia of Finance 2009
[3] J. Bion-Nadal (2009)*. Time consistent dynamic risk processes, Stochastic processes and their applications, vol 119, issue 2 p:633-654.
[4] J. Bion-Nadal (2009)*. Bid-Ask dynamic pricing in nancial markets with transaction costs and
liquidity risk, To appear in Journal of mathematical economics.
[5] B. Bouchard, R. Elie et N. Touzi (2009). Discrete-Time Approximation of BSDEs and Probabilistic
Schemes for Fully Nonlinear PDEs, Radon Series on Computational and Applied Mathematics.
[6] B. Bouchard, R. Elie et N. Touzi (2009). Stochastic Target Problems with Controlled Loss, SIAM
Journal on Control and Optimization.
[7] A. Cretarola, F. Gozzi, H. Pham, and P. Tankov (2009). Optimal consumption policies in illiquid markets. To appear in Finance and Stochastics.
[8] R. Cont and P. Tankov (2009)*. Constant proportion portfolio insurance in the presence of jumps in asset prices, Mathematical Finance, 19, pp. 379{401.
[9] N. El Karoui and Y. Jiao (2009). Stein's method and zero bias transformation for CDO tranche pricing, Finance and Stochastics (2009) 13:151-180
[10] A. Galichon (2009)*. The VaR at Risk, International Journal on Theoretic and Applied Finance,
(special issue on the occasion of the 2008 X-Columbia conference in Paris)
[11] P. Imkeller, G. Dos Reis (2009). Path regularity and explicit convergence rate for BSDE with truncated
quadratic growth, To appear in Stochastic processes and their applications
[12] P. Imkeller, G. Dos Reis and J. Zhang (2009)*. Results on numerics for FBSDE with drivers of quadratic growth, To appear in "Special Springer volume in honour of Eckhard Platen's 60th birth-day"
[13] H. Pham and P. Tankov (2009)*. A coupled system of integrodierential equations arising in liquidity risk model, Applied Mathematics and Optimization, 59, pp.147{173.
[14] A.Porchet , N. Touzi and X. Warin (2009). Valuation of a powerplant under production constraints and markets incompleteness, Mathematical Methods of Operations research, Volume 70, Issue 1, Page 47-75.
[15] M. Rosenbaum (2009)*. Integrated volatility and round o error, Bernoulli 15 (03) p 687-720.
[16] M. Rosenbaum (2009). First order p-variation and Besov spaces, Statistics and Probability Letters
79 (01) p 55-62
[17] M. Rosenbaum (2009)*. A new microstructure noise index, to appear in Quantitative Finance.
[18] M. Rosenbaum, A. Tsykabov (2009). Sparse Recovery under Matrix Uncertainty, to appear in Annals of Statistics.
[19] M. Soner et N. Touzi (2009). The Dynamic Programming Equation for Second Order Stochastic
Target Problems, SIAM J. Control Optim. Volume 48, Issue 4, pp. 2344-2365.
[20] P. Tankov (2009)*. Pricing and hedging gap risk, to appear in Journal of Computational Finance.
[21] P. Tankov and E. Voltchkova (2009)*. Asymptotic analysis of hedging errors in models with jumps,
Stochastic processes and their applications, 119, pp. 2004{2027.
[22] P. Tankov and E. Voltchkova (2009)*. Jump-diusion models: a practitioner's guide, Banque etMarches.
[BGM08] E. Benhamou, E. Gobet, and M. Miri. Expansion formulas for European options in a localvolatility model. Forthcoming in International Journal of Theoretical and Applied Finance. Available at http://hal.archives-ouvertes.fr/hal-00325939/fr/, 2008.
[BGM09a] E. Benhamou, E. Gobet, and M. Miri. Analytical formulas for local volatility model with stochastic rates. Rapport de recherche, LJK, France, October 2009. submitted.
[BGM09b] E. Benhamou, E. Gobet, and M. Miri. Smart expansion and fast calibration for jump diusion. Finance and Stochastics, 13(4):563{589, 2009.
[BGM09c] E. Benhamou, E. Gobet, and M. Miri. Time dependent Heston model. In revision for SIAM Journal on Financial Mathematics, available at http://hal.archives-ouvertes.fr/hal-00370717/fr/,2009.
[FPS00] J.P. Fouque, G. Papanicalaou, and R. Sircar. Derivatives in nancial Markets with stochastic volatility. Cambridge University Press, 2000.
[GL09] E. Gobet and C. Labart. Solving BSDE with adaptive controle variate. In revision at SIAM Numerical Analysis, 2009.
[GM09a] E. Gobet and A. Makhlouf. L2-time regularity of BSDEs with irregular terminal functions.
In revision for Stochastic Processes and their Applications, available at http://hal.archives-ouvertes.fr/hal-00291768/fr/, 2009.
[GM09b] E. Gobet and A. Makhlouf. The tracking error rate of the Delta-Gamma hedging strategy.
Preprint, available at http://hal.archives-ouvertes.fr/hal-00401182/fr/, 2009.
[GM10] E. Gobet and S. Menozzi. Stopped diusion processes: Boundary corrections and overshoot.
Stochastic Processes and Their Applications, 120:130{162, 2010.
[Gob09] E. Gobet. Handbook of Numerical Analysis, Vol. XV, Special Volume: Mathematical Modeling and Numerical Methods in Finance, chapter Advanced Monte Carlo methods for barrier and related exotic options, pages 497{528. Elsevier, Netherlands: North-Holland, 2009.
[HKLW02] P. Hagan, D. Kumar, A. Lesniewski, and D. Woodward. Managing smile risk. Willmott Magazine, pages 84{108, 2002.
[KT01] N. Kunitomo and A. Takahashi. The asymptotic expansion approach to the valuation of interestrate contingent claims. Mathematical Finance, (117-151), 2001.
[Wat87] S. Watanabe. Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Annals of Probability, 15(1):1{39, 1987.

Pré-Publications 2009 (Polytechnique)

[23] R. Aid, O. Feron, N. Touzi et C. Vialas (2009). An arbitrage-free interest rate model consistent with
economic constraints for long-term asset liability management. Submitted to Bankers, Markets andInvestors.
[24] E.Bacry, A.Gloter, M.Homann et J.F.Muzy (2009). Estimation of the multifractal spectrum in a mixed asymptotic framework, submitted to Annals of Applied Probability
[25] P. Barrieu, H. Bensusan, N. El Karoui, C. Hillairet, S. Loisel, C. Ravanelli, Y. Salhi (2009)*. Understanding,
Modeling and Managing Longevity Risk : Key issues and Main Challenges, submitted to Scandinavian Actuarial Journal
[26] A.Benabid, H.Bensusan et N.El Karoui (2009)*. Wishart Stochastic Volatility: Asymptotic Smile and Numerical Framework. In revision for Quantitative Finance.
[27] A.Benabid, H.Bensusan et N.El Karoui (2009)*. Short term Smile In general Whishart Stochatic Volatility Model.
[28] B. Bouchard et N. Touzi (2009). Weak dynamic programming principle for viscosity solutions, submitted to SIAM Journal on Control and Optimization.
[29] M. Broden, P. Tankov (2009)*. Errors from discrete hedging in exponential Levy models: the L2 approach, submitted to Finance and Stochastics.
[30] G. Carlier, A. Galichon, F.Santambrogio (2009). From Knothe's transport to Brenier's map and a continuation method for optimal transport, in revision for SIAM Journal on Mathematical Analysis.
[31] L.Carasso, N.El Karoui et Jan Obloj (2009). On Azema-Yor processes, their optimal properties and the Bachelier Drawdown equation, submitted to Annals of Probability.
[32] G. Chemla, R. Aid, A. Porchet et N. Touzi (2009). Vertical integration and Risk management in competitive markets of non-storable goods. In revision for Management Science.
[33] V. Chernozhukov, I. Fernandez-Val, A. Galichon (2009). Quantile and Probability Curves without Crossing, in revision for Econometrica.
[34] D. Crisan, K. Manolarakis et N. Touzi (2009). On the Monte Carlo simulation of BSDEs: an improvement
on the Malliavin weights. In revision for Stochastic Processes and their Applications.
[35] I.Ekeland, A. Galichon, M. Henry (2009)*. Comonotonic measures of multivariate risks, in revision for Mathematical Finance.
[36] N. El Karoui, M. Jeanblanc and Y. Jiao (2009). The conditional density approach, in revision for Stochastic Processes and their Applications.
[37] N. El Karoui, M. Jeanblanc and Y. Jiao (2009). Modelling of succesive Default events, a density buttom-up approach.
[38] A. Fahim, N. Touzi, et X. Warin (2009). A Probabilistic Numerical Method for Fully NonlinearParabolic PDEs, in revision for Annals of Applied Probability.
[39] A. Galichon, M. Henry (2009). Inference in models with multiple equilibria , overhaul of the 2006 working paper "Inference in Incomplete Models," in revision for Review of Economic Studies.
[40] A. Galichon, M. Henry (2009). Dilation Bootstrap: A methodology for constructing condence regions with partially identied models, in revision for Journal of Econometrics.
[41] M. Homann, M. Rosenbaum, N. Yoshida (2009)*. Estimation of the lead-lag parameter between two nancial assets from non-synchronous data, submitted to Finance and Stochastics.
[42] A. Kohatsu-Higa and P. Tankov (2009)*. Jump-adapted discretization schemes for Levy-driven SDEs, in revision for Stochastic Processes and their Applications.
[43] A.Kozhemyak, E.Bacry, J.F.Muzy (2009). Log-Normal continuous cascades: aggregation properties and estimation. Application to nancial time-series, submitted to Quantitative Finance.
[44] C.Y. Robert, M. Rosenbaum (2009). On the limiting spectral distribution of the covariance matrices of time-lagged processes, submitted to Journal of Multivariate Analysis.
[45] C.Y. Robert. M. Rosenbaum (2009)*. On the microstructural hedging error, submitted to SIAM SIFIN.
[46] C.Y. Robert, M. Rosenbaum (2009)*. Volatility and covariation estimation when microstructure noise and trading times are endogenous, submitted to Mathematical Finance.
[47] C.Y. Robert, M. Rosenbaum (2009)*. A new approach for the dynamics of ultra high frequency data: the model with uncertainty zones, submitted to Journal of Financial econometrics .
[48] P. Tankov (2009)*. Pricing and hedging in exponential Levy models: review of recent results submitted to Paris-Princeton lecture notes on Mathematical Finance.

Publications 2009 (Ecole des Ponts)

[49] A. Alfonsi and B. Jourdain, (2009)*. Exact volatility calibration based on a Dupire-type Call-Put duality for perpetual American options,Nonlinear Dierential Equations and Applications, Vol. 16, No. 4, pp. 523-554.
[50] A. Alfonsi, A. Fruth, A. Schied, (2010)*. Optimal execution strategies in limit order books with general shape functions. Quantitative Finance DOI:10.1080/14697680802595700.
[51] A. Alfonsi, (2009)*. High-order discretization scheme for the CIR process: application to the Heston model. Mathematics of Computation, Vol. 79, No. 269, pp. 209-237.
[52] A. Alfonsi, (2010)*. Cox-Ingersoll-Ross (CIR) model, Encyclopedia in Finance, to appear in 2010.
[53] B. Jourdain, J. Lelong, (2009)*. Robust Adaptive Importance Sampling for Normal Random Vectors,Ann. Appl. Probab. 19(5), pp 1687-1718.
[54] B. Jourdain, (2009)*. Adaptive variance reduction techniques in nance, Advanced Financial Modelling, Radon Series Comp. Appl. Math 8, Ed. by H. Albrecher, W. Runggaldier and W. Schacher-mayer, de Gruyter, pp. 205-222.
[55] P. Etore, B. Jourdain*. Adaptive optimal allocation in stratied sampling methods, to appear in Methodology and Computing in Applied Probability.
[56] P. Etore, G. Fort, B. Jourdain, E. Moulines*. On Adaptive Stratication, to appear in Annals of operations research.

Pré-publications 2009 (Ecole des Ponts)

[57] A. Alfonsi, A. Schied, (2009)*. Optimal execution and absence of price manipulations in limit order book models, June 2009, submitted.
[58] A. Alfonsi, A. Schied, A. Slynko, (2009)*. Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem, October 2009, submitted.
[59] A. Alfonsi, J. Lelong, (2009)*. A closed-form extension to the Black-Cox model, September 2009.
[60] A. Alfonsi, (2009)*. An introduction to the multiname modelling in credit risk (Survey that will be part of a book edited by T. Bielecki, D. Brigo and F. Patras).
[61] B. Jourdain, M. Sbai, (2008)*. Coupling Index and Stocks, December 2008, submitted.
[62] B. Jourdain, M. Sbai, (2009)*. High order discretization schemes for stochastic volatility models, August 2009
[63] B. Jourdain, M. Vellekoop, (2009)*. Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends, November 2009, submitted

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