Progress Made and Results Obtained
Work on our research program (up to 2003) has already lead to many articles and working papers. [Detailed references appear in our earlier project CV].
1. Asset Pricing and Portfolio Models
1a. Derivative Pricing
The project on derivative pricing has lead to the publication of 8 articles [Broadie, Detemple, Ghysels and Torrès (2000a, 2000b), Detemple (2001), Detemple, Feng and Tian (2003), Detemple and Osakwe (2000), Detemple and Serrat (2003), Detemple and Tian (2002), Garcia and Gençay (2000)] and 1 discussion papers [Garcia, Luger and Renault (2001)].
1b. Dynamic Asset Allocation
The project on dynamic asset allocation resulted in [Detemple, Garcia and Rindisbacher (2003a), Detemple and Karatzas (2003), Bodie, Detemple, Otruba and Walter (2004)] and 9 discussion papers [Detemple, Garcia and Rindisbacher (2003b, 2004a, 2004b, 2004c, 2004d, 2004) Detemple and Rindisbacher (2004), Garcia, Luger and Renault (2001 Garcia, Luger and Semenov (2002) Rindisbacher (2002)].
2. Statistical Models for Financial Time Series
Our work on statistical models for financial time series [such as dynamic factor models, GARCH-type and stochastic volatility models, duration models has led to the publication of 12 articles [Garcia and Bonomo (2001a, 2001b), Garcia, Ghysels and Renault (2003), Garcia and Renault (2001), Garcia and Schaller (2002), Meddahi (2002, 2003), Meddahi and Renault (2002), Patilea and Renault (2002), Renault (2000, 2002), Renault and Alami (2000), Renault, Pastorello and Touzi (2000)] and 18 discussion papers [Andersen, Bollerslev and Meddahi (2002a, 2002b), Bandi And Perron (2001), Campbell, Meddahi and Sentana (2002), Garcia, Lewis and Renault (2001), Garcia, Luger and Renault (2001a, 2001b), Meddahi (2001a, 2001b, 2002a, 2002b, 2002c, 2002d), Linton and Perron (2001), Moon and Perron (2002a), Perron (2001a, 2001b), Renault, Garcia and Ghysels (2001)].
3. Inference in Financial Time Series
3a. Weak Linear ARMA Representations and Non-Linear
Our work on nonlinear time series models for financial analysis and weak ARMA representations has produced 6 articles [Blais, MacGibbon and Roy (2000), Duchesne and Roy (2001, 2003), Dufour and Torrès (1999), ), El Himdi, Roy and Duchesne (2003), Pham, Roy and Cédras (2001)] and 7 discussion papers [Bonnal and Renault (2001), Bontemps and Meddahi (2002a, 2002b), Bouhaddioui and Roy (2002a, 2002b), Dufour and Pelletier (2002), Dufour and Trognon (2002)].
3b. Statistical inference with weak identification
Our work on inference under conditions of weak identification (or with weak instruments) has lead to the publication of 6 articles [Carrasco, Florens and Renault (2003), Dufour (2000, 2001,2003), Dufour and Jasiak (2001), Perron (2002)] and 7 discussion papers [Abdelkhalek and Dufour (2002), Darolles, Florens and Renault (2000), Dufour and Khalaf (1999a), Perron (2000), Khalaf and Kichian (2002), Khalaf, Saphores and Bilodeau (2002). Moon and Perron (2002b)].
3c. Monte Carlo Inference
Our work on Monte Carlo test methods has lead up to now to the publication of 11 articles [Dufour and Farhat (2002), Dufour and Khalaf (2001a, 2001b, 2001c, 2002), Dufour, Khalaf, Bernard and Genest (2002), Dufour and Neifar (2002), Dufour, Pelletier and Renault (2002), Ghysels, Khalaf and Vodounou (2002), Khalaf and Kichian (2002), Khalaf, Pellletier and Saphores (2002)] and 7 discussion papers [Beaulieu, Dufour and Khalaf, (2002a, 2002b), Dufour (2001), Dufour and Farhat (2001a, 2001b, 2001c), Dufour and Valéry (2002)].
Concerning the various projects described in the present proposals, we can already mention the following outputs (since 2003). [Detailed references are available in Section 8]
A. Mathematical methods for portfolio management and option pricing
9 articles [Bodie, Detemple, Otruba and Walter (2004), Detemple, Feng and Tian, (2003), Detemple, Garcia and Rindisbacher (2003a, 2003b, 2004a, 2004b, 2004c), Garcia, Ghysels and Renault (2003), Garcia, Luger and Renault (2003)] and 5 discussion papers [Chabi-Yo, Garcia and Renault (2004), Detemple, Garcia and Rindisbacher (2004d), Detemple and Rindisbacher (2004), Garcia, Luger and Renault (2003), Garcia, Renault and Tsafack (2003)]
B. Volatility modelling
7 articles [Andersen, Bollerslev and Meddahi (2003a, 2003b), Meddahi (2003), Meddahi and Renault (2004), Meddahi, Renault and Werker (2004), Pastorello, Patilea and Renault (2003), Perron (2004)] and 2 discussion papers [Comte, Coutin and Renault (2004), Renault and Werker (2004)]
C. Long memory in finance
2 articles [Moon and Perron (2004a, 2004b)]
D. Structural modelling in finance
7 articles [Bontemps and Meddahi (2003), Carrasco, Florens Renault (2003), Croux, Renault, Werker (2004), Dufour (2003), Dufour and Taamouti (2003a), Khalaf and Kichian (2004a, 2004b)] and 8 discussion papers [Bolduc, Khalaf and Moyneur (2004), Bonnal and Renault (2004), Dufour, Khalaf and Kichian (2004), Dufour and Khalaf (2003), Dufour and Taamouti (2003b, 2003c, 2004), Khalaf and Kichian (2004)]
E. Linear methods for nonlinear time series models
7 articles [Duchesne and Roy (2003, 2004), Dufour, Pelletier and Renault (2004), El Himdi, Roy and Duchesne (2003), Francq, Roy and Zakoïan (2003), Ghysels, Khalaf and Vodoumou (2003), Pham, Roy and Cédras (2003)] and 6 discussion papers [Bouhaddioui and Roy (2003a, 2003b), Mélard, Roy and Saidi (2004), Moon and Perron (2004a, 2004c), Moon, Perron and Phillips (2003)]
F. Statistical assessment of asset pricing models
5 articles [Beaulieu, Dufour and Khalaf (2004), Dufour, Farhat and Khalaf (2004), Dufour and Jouini (2004a), Dufour, Khalaf and Beaulieu (2003), Dufour, Khalaf, Bernard and Genest (2004)] and 10 discussion papers [Beaulieu, Dufour and Khalaf (2003a, 2003b, 2003c, 2004a, 2004b), Dufour and Jouini (2003), Dufour, Khalaf and Beaulieu (2003), Dufour and Kim (2004), Dufour and Neifar (2003), Garcia, Renault and Veredas (2003)]
G. Mathematical and statistical modelling of energy markets
1 article [Khalaf, Saphores and Bilodeau (2003)] and 2 discussion papers [Bernard, Dufour, Khalaf and Kichian (2004), Bernard, Idoudi, Khalaf and Yélou (2004) ]
Significance of the results obtained in terms of their industrial relevance
This project falls under the mathematics of risk modeling and resource management and contains both core research and technology transfer components. It aims ultimately at providing risk management offices with new financial models and econometric tools for better trading strategies. The team's objective is to develop and implement new mathematical and statistical tools for pricing derivatives, hedging risk exposures and managing portfolios. This involves, in particular, the development of models for derivative security pricing and hedging with time-series and cross-sectional restrictions (panel structure), as well as the implementation of intertemporal portfolio allocation rules based on continuous time diffusion models and simulations.
This research program is pursued in the context the Centre for Interuniversity Research and Analysis on Organizations (CIRANO; http://www.cirano.qc.ca). This research center is a highly successful and original venture whose specific purpose is to foster close cooperation between university researchers and non-academic institutions (private and public). CIRANO is a multidisciplinary, multiuniversity and intersectorial network of researchers who study economic and managerial problems, using state-of-the-art mathematical and statistical techniques, especially in the field of Finance. The CIRANO model consists in working on a research program of interest to a number of non-academic partners. The partners supply financing to the Center. In return, they are kept informed of the results of the research and invited to various transfer activities (seminars, conferences, individual meetings with researchers). In some cases, the exchange takes the form of a direct collaboration with CIRANO researchers.
CIRANO partners with a special interest for research in Finance include: AXA (Insurance), the Bank of Canada, Caisse de depot et placement du Québec, the Laurentian Bank of Canada, the National Bank of Canada, the Royal Bank of Canada, Bank of Montreal, Bell Canada, Hydro-Québec, Desjardins, the Montreal Stock Exchange, the Ministère des Finances (Québec), and Raymond, Chabot, Grant, Thornton. In addition, CIRANO was entrusted in 1998 with the research facet of Montreal’s mathematical finance institute, the Institut de finance mathématique de Montréal (IFM2).
In the case of this MITACS project, the partnership with non-university organizations has taken several forms. Let us mention the following.
(A) The team has developed various pieces of software, including a general-purpose program able to implement and simulate a wide array of option-pricing formulas based on different. Besides the well known Black-Scholes model, the software deals with European or American options whose payoff can be vanilla, barrier, look-back or Asian. The pricing functions are based on closed-formed, Monte-Carlo simulation and finite-difference. Others models such as stochastic volatility and stochastic volatility with jump are taken into consideration. In addition to pricing methods, components which intend to estimate models parameters were implemented according to the indirect inference method and the efficient method of moments.
(B) The team runs a very active seminar series on topics in mathematical finance econometrics which is well attended by the Montreal financial community. Seven major conferences for researchers and practitioners have also been organized: (1) Intertemporal Asset Pricing Conference (October 1999); (2) Econometric Methods and Financial Markets (September 1999); (3) Conference-Workshop on Financial Mathematics and Econometrics (June 2001); (4) Resampling Methods in Econometrics (October 2001); (5) Simulation Based and Finite Sample Inference in Finance (May 2003); (6) 2003 Financial Econometrics Conference (May 2003); (7) 2004 Financial Econometrics Conference (May 2004).
(C) Students that worked on the project have found employment in various financial and related institutions, in particular CIRANO business partners such as: the National Bank of Canada, the Royal Bank of Canada, Gaz Métro, and the Caisse de dépôt et Placement du Québec. Students have also made internships with the Laurentian Bank of Canada and Hydro-Québec.
(D) The project has helped to set up a new graduate program (Master Degree in Mathematical and Computational Mathematics) at the Université de Montréal, which is specifically designed for the financial community in the area of financial mathematics.