Mathematics of Information Technology and Complex Systems


Project Highlights



Team Members

Partner Organizations








  • Project Title: Mathematical and Statistical Methods for Financial Modelling and Risk Management



  • Short project description: This research project deals with the mathematics of risk modeling and resource management. The objective is to develop and implement new mathematical and statistical tools for pricing derivatives, hedging risk exposures and managing portfolios. The project studies two general themes:
        (A) portfolio management and pricing of derivatives,
        (B) statistical modelling and inference for financial time series.


  • Project description: This research project studies mathematical and statistical methods for analyzing financial data and helping practitioners of risk modeling and resource management. An important objective is to develop and implement new mathematical and statistical tools for pricing derivatives, hedging risk exposures and managing portfolios. Two general themes are covered: (A) portfolio management and pricing of derivatives, (B) statistical modelling and inference for financial time series.
    The first theme covers three topics: (1) optimal portfolio design when state variables follow mixed jump-diffusion processes; (2) option valuation based on generalized models involving latent variables with jump processes; (3) hedge fund strategies and portfolio allocation.
    The second theme considers several problems related to the statistical analysis of financial time series: (1) volatility modelling: realized volatility methods, stochastic volatility with transaction time risk, robust statistical inference in the presence of random volatility of unknown form; (2) long memory models in finance: long memory in volatility, long memory in continuous time arbitrage based asset pricing; (3) structural modelling in finance: statistical inference on overidentified models, inverse problems, weak instruments in finance; (4) linear methods for nonlinear time series models; (5) statistical assessment of asset pricing models; (6) mathematical statistical modelling of energy markets.
    Both research themes will lead to the development of software for financial modelling and analysis in association with our industrial partners.
    Participants to the project include several well-known researchers in mathematical finance, statistics and econometrics: R. Garcia, E. Renault, N. Meddahi, B. Perron, R. Roy (Un. de Montréal), J. Detemple (Boston University), L. Khalaf (Un. Laval) and M. Rindisbacher (Un. of Toronto). The project will be pursued in association with the Finance branch of CIRANO and its partners [AXA, Laurentian Bank of Canada, Bank of Montreal, Caisse de dépôt et de placement du Québec, National Bank of Canada, RBC, Bell Canada, Hydro-Québec, Desjardins, Montreal Stock Exchange, the Ministère des Finances (Québec), Raymond, Chabot, Grant, Thornton, and the Institut de finance mathématique de Montréal].


  • Recent developments that are worth notice include the following:


    1. During the year 2005-2006, Jean-Marie Dufour received seven distinctions for his research work partially supported by MITACS.
      1. Election as Fellow of the American Statistical Association, 2005.
        "For outstanding contributions to statistical methodology in econometrics, exact distribution-free and parametric methods, time series analysis, causality analysis, and statistical inference in weakly identified models; and for service to the profession."
      2. The Marcel-Vincent Prize, from Association francophone pour le savoir (Acfas), 2005, funded by Bell Canada. For research in econometrics.
      3. The Konrad Adenauer Research Award, from the Alexander von Humboldt Foundation (Germany), 2005.
        "This award, established through the generosity of the Alexander von Humboldt Foundation, is made to highly qualified Canadian scholars whose research work (…) has earned international recognition and who are among the group of leading scholars in their respective area of specialization."
      4. The Killam Prize 2006 for Social Sciences, Killam Trust and Canada Council for the Arts. For research in econometric methods in macroeconomics and finance.
        Killam Prizes are "Canada's most distinguished annual awards for outstanding career achievements in engineering, natural sciences, humanities, social sciences and health sciences."
      5. A Fellowship from the John Simon Guggenheim Memorial Foundation (U.S.A.) for 2006-2007. For research in econometrics and statistics.
      6. Personality of the week La Presse / Radio-Canada ("Personnalité de la semaine La Presse / Radio-Canada"), April 23, 2006. A full page article published by the newspaper La Presse on April 23, 2006.
      7. Officer of the National Order of Québec [Officier de l'Ordre national du Québec], Government of Québec, 2006. The order will be conferred on June 20, 2006.
        "The Ordre national du Québec is the highest distinction conferred by the Government of Québec. In this way, the Prime Minister grants to remarkable personalities the title of Grand Officer, Officer or Knight of the Order." This honour is conferred "for outstanding achievements in most fields."
    2. In 2005, Silvia Gonçalves was promoted Associate Professor in economics (econometrics) at the Université de Montréal.
    3. Lynda Khalaf was promoted Full Professor at the Department of Economics, Université de Laval.
    4. Benoit Perron has become an Associate Editor of Empirical Economics and a member of the Scientific Board of the Institut de finance mathématique (IFM2).
    5. Marcel Rindisbacher was promoted Associate Professor at the Rotman School of Management, University of Toronto.


    1. René Garcia was awarded the newly created Hydro-Québec Chair in Integrated Risk Management and Mathematical Finance on May 28, 2003 at the université de Montréal.
    2. During the year 2002-2003, Jean-Marie Dufour was President of the Canadian Economics Association. On May 31, 2003, in Ottawa, he gave his Presidential address on statistical methods for economic and financial analysis. The title of his talk was: “Identification, weak instruments and statistical inference in econometrics” (slides).
    3. Éric Renault was awarded on May 14, 2003, the Marcel Dagenais Prize for excellence in research by the Société canadiene de science économique. The previous recipent of this prize (which is awarded only once every three years) was also awarded to a member of our team (Jean-Marie Dufour).
    4. Éric Renault was awarded the Canada Research Chair in Financial Econometrics at the Université of Montreal. The new chair’s objective is to advance the study of financial econometrics and develop innovative applications for risk management, asset pricing and the economics of uncertainty associated with a number of technological issues. This research will greatly benefit banking regulators and researchers of financial institutions and markets who are challenged by increasingly complex issues related to risk management and financial markets or derivative assets.
    5. As holder of the Canada Resarch Chair in Econometrics (since 2001), Jean-Marie Dufour has obtained a geant from the Canada Research Foundation for starting a “Mathematical Methods and Financial Econometrics Laboratory” based at CIRANO, which will be used for research in mathematical finance and financial econometrics.
    6. René Garcia was nominated Scientific Director of CIRANO.
    7. The new Journal of Financial Econometrics just came out! This new journal focuses on financial econometrics, a field that has become one of the most active areas of research in econometrics and is a speciality shared by many CIRANO researchers. It aims at reflecting and advancing the relationship between econometrics and finance, both at the methodological and at the empirical levels. More precisely, the statistical issues linked to the various aspects of asset pricing and risk management represent its core focus. René Garcia and Éric Renault are the editors-in-chief of the Journal. The Journal itself is actively managed from CIRANO’s offices. In the spirit of active transfer and liaison, both key CIRANO goals, the Journal also features a Practitioners' Corner. This section emphasizes the practical side of each issue's content and places the articles within a broader perspective. The Journal of Financial Econometrics's electronic version now has its own Web site with the Oxford University Press.
    8. The Finance group of CIRANO is proud to announce its partnership with the Professional Risk Manager’s International Association (PRMIA) which has launched its new regional Montreal Chapter a few months ago. PRMIA is a non-profit global association with the mission to provide a free and open forum for the promotion of sound risk management standards and practices globally. Its objectives include: connecting practitioners, researchers, students and others interested in the field of risk management; driving the integration of practice and theory and certifying the credentials of risk managers with the globally recognized PRMIA Professional Risk Manager certification. CIRANO and PRMIA make excellent partners as they both promote a better communication and a more efficient transfer of knowledge between researchers and companies. As David Stréliski, regional director of PRMIA Montreal, puts it: “This association is an important step towards establishing a common and accessible forum to bring together academics and professionals, theoreticians and practitioners, around today’s key questions in finance, financial engineering and risk management. By working together efficiently, we will be able to establish Montreal as an excellence center for the development and application of innovative ideas in these fields.” Among its activities, PRMIA will be organizing a Career Day focused Career Perspectives in Finance, Risk Management and Financial Engineering. This event will allow professionals in these fields to give students a description of their typical activities in their respective professions. More information on PRMIA’s activities is available on their website