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Feynman-Kac measures and Interacting Particle systems :

Selected applications on : Financial Mathematics & Econometrics

(see also : selected studies, publications & MLSS 08 Lecture notes, 2011-Sino-French Summer Institute (lecture 1, lecture 2, and lecture 3) & other application areas)


This webpage presents a selected series of articles related to the use of particle methods in Mathematical finance, including This list of topics is clearly far from being exhaustive, and it is partially biased towards my work on stochastic particle models. More references and links to this subject can be added on demand. This webpage also contains some articles on the particle and sequential Monte Carlo methodology, and the performance analysis of these algorithms. The forthcoming book on numerical methods in Finance also contains new developments on particle methods in risk analysis, option pricing, and sensibility measure computations
The software BIIPS is a general software developed by the INRIA team ALEA for bayesian inference with interacting particle systems, a.k.a. Sequential Monte Carlo methods. A demonstration of the BiiPS software for estimating the stochastic volatility of financial data can be found in




Surveys, Ph.D. thesis



  • A survey of sequential Monte Carlo methods for economics and finance (Drew Creal, University of Chicago, Booth School of Business 2009)

  • Estimating default probabilities for CDO's: a regime switching model
    (Jantine Koebrugge, Ph.D. University of Twente, Enschede, The Netherlands 2011)

  • R. Carmona, P. Del Moral, P. Hu, N. Oudjane An introduction to particle methods in finance in Numerical Methods in Finance (43p.).
    Springer New York, Series : Proceeding in Mathematics, (to appear 2012).

  • Sequential Monte Carlo Methods for Option Pricing (A. Jasra, P. Del Moral, Stoch. Analysis and Appl., 2011)

  • Pierre Del Moral, Peng Hu, Liming Wu
    On the concentration properties of Interacting particle processes HAL-INRIA RR-7677 (2011),
    Foundations and Trends in Machine Learning, Vol. 3, No. 3 - 4, 225-389 (2012). (online article, 167 pages)


    Risk analysis


  • Interacting Particle Systems for the Computation of Rare Credit Portfolio Losses Rene Carmona, Jean-Pierre Fouque, Douglas Vestal

  • Interacting path systems for credit portfolios risk analysis (P. Del Moral, Fr. Patras, HAL-INRIA 7169, 2010)

  • Particle methods for the estimation of credit portfolios loss distribution (R. Carmona, S. Crepey, Bendheim Center for Finance ORFE, Princeton University, and Evry Val d'Essonne University 2009)

  • Estimating default probabilities for CDO's: a regime switching model (Jantine Koebrugge, Ph.D. University of Twente, Enschede, The Netherlands 2011)

  • Filtering Methods (Andras Fulop, ESSEC Business School, Paris)


    Filtering and estimation


  • Interacting Particle Systems for the Computation of CDO Tranche Spreads with Rare Defaults Rene Carmona, Jean-Pierre Fouque, Douglas Vestal

  • Estimation procedure for a hidden Markov chain model with applications to finance, climate data and earthquake analysis (I. Florescu and F. Levin, Stevens Institute of Technology)

  • Recovering Volatility From Option Prices by Evolutionnary Optimization Sana Ben Hamida, Rama Cont (CNRS et Ecole Polytechnique Paris, France)

  • Particle Methods in Filtering and Finance R. Carmona (Princeton-Bendheim Center for Finance)

  • Simulation Methods for Non-linear and Non-Gaussian Models in Finance R. Casarin (Department of Economics, University of Venice and Department of Mathematics, University of Paris Dauphine)

  • Business Cycle and Stock Market Volatility. A Particle Filter Approach R. Casarin, C.Trecroci (Dpt. of Economics, Brescia and Glasgow Univ.)

  • Variable selection using non-standard optimization G. Kapetanios (Department of Economics, Queen Mary, University of London)

  • Cluster analysis of panels datasets using non-standard optimization and information criteria G. Kapetanios (Department of Economics, Queen Mary, University of London)

  • Conditional likelihood estimators for hidden Markov models and stochastic volatility models (V. Genon-Catalot, T. Jeantheau, C. Laredo; Marne la Vallee University and INRA Jouy en Josas)

  • Optimal Filtering of Jump diffusions : Extracting Latent States from Assets Prices (M. Johannes, N. Polson, J. Stroud; Columbia Univ. Chicago Univ. and Pensylvania Univ.)

  • A study about the existence of the leverage effect in Stochastic Volatility models (I. Florescu,, C. G. Pasarica, Stevens Institute of Technology, Hoboken 2008)

  • Estimation procedure for a hidden Markov chain model with applications to nance, climate data and earthquake analysis (I. Florescu, F. Levin, Stevens Institute of Technology, Hoboken 2008)

  • Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering (Sheheryar Malik and Michael K Pitt, Dept. of Economics, Warwick Univ. 2009)

  • State-Observation Sampling and the Econometrics of Learning Models (Laurent E. Calvet and Veronika Czellar Department of Finance, HEC Paris, 2011)

  • Particle methods for the estimation of credit portfolios loss distribution (R. Carmona, S. Crepey, Bendheim Center for Finance ORFE, Princeton University, and Princeton University, and Evry Val d'Essonne University 2009)

  • Bayesian inference based only on simulated likelihood: particle Filter analysis of dynamic economic models (Thomas Flury, Neil Shephard Oxford-Man Institute, University of Oxford 2008)

  • Estimating Stochastic Volatility via Filtering for the Micro-movement of Asset Prices (Yong Zeng, Department of Mathematics and Statistics, University of Missouri at Kansas City 2002)

  • Inferencia de la volatilidad de retornos financieros usando filtro de particulas (Felipe Arturo Tobar Henriquez, Ph.D. Univ. Chile 2010)

  • A Branching Particle Approximation to a Filtering Micromovement Model of Asset Price (Jie Xiong, and Yong Zeng, Department of Mathematics, University of Tennessee at Knoxville 2010)

  • Bayesian Filtering for Jump-Diffusions with Applications to Stochastic Volatility (Andrew Golightly, Newcastle University 2007)



    Option pricing & Portfolio optimization


  • A Monte Carlo Method for Portfolio Optimization under Partially Observed Stochastic Volatility (R. Desai, T. Lele, F. Viens; Purdue Univ.)

  • P. Del Moral, P. Hu, N. Oudjane, Br. Rémillard. On the Robustness of the Snell envelope (HAL-INRIA RR-7303 2010) [35p].
    SIAM Journal on Financial Mathematics, vol.2, 587-626 (2011).

  • P. Del Moral, B. Rémillard, S. Rubenthaler. Monte Carlo approximations of american option that preserve monotonicity and convexity.
    Numerical Methods in Finance (28p.). Springer New York, Series : Proceeding in Mathematics, (to appear 2012).

  • P. Del Moral, P. Hu, and N. Oudjane. Snell Envelope with path dependent multiplicative optimality criteria, HAL-INRIA RR 7360 [18p] (2010).

  • Stochastic Volatility and Option Pricing with Long-Memory in Discrete and Continuous Time (Alexandra Chronopoulou, Frederi G. Viens, Institut Elie Cartan, INRIA Nancy Grand-Est, and Department of Statistics, Purdue University, 2011)

  • Stochastic Volatility : Option Pricing using a Multinomial Recombination Tree (I. Florescu, F. Viens; Purdue Univ.)

  • Portfolio Optimization with Discrete Proportional Transaction Costs under Stochastic Volatility (Ha-Young Kim, F. Viens; Purdue Univ. 2009)

  • Selection of an Optimal Portfolio with Stochastic Volatility and Discrete Observations (Natalia V. Batalova, Vassili Maroussov, Frederi G. Viens, Bank of America Securities, London, and Purdue University)

  • Estimation and Pricing under Long-Memory Stochastic Volatility (Alexandra Chronopoulou, Frederi G. Viens, Purdue University)





    Econometrics


  • Construction d'un algorithme d'acceleration de la methode des simulations dans les simulations pour le calcul du capital economique Solvabilite II (Laurent Devineau, Stephane Loisel, Université de Lyon 1, Laboratoire de Science Actuarielle et Financiere, 2009)

  • Construction of an acceleration algorithm of the nested simulations method for the calculation of the solvency II Economic capital (Laurent Devineau, Stephane Loisel, Université de Lyon 1, Laboratoire de Science Actuarielle et Financiere)

  • Intra-daily variations in volatility and transaction costs in the Credit Default Swap market (Andras Fulop, Laurence Lescourret, ESSEC Business School 2009)

  • On housing booms and credit market conditions: A state space model (Helmut Herwartz, Fang Xu, Christian-Albrechts-University at Kiel 2011)