Journal of Financial Econometrics Advance Access originally published online on September 9, 2008
Journal of Financial Econometrics 2008 6(4):407-458; doi:10.1093/jjfinec/nbn011
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Econometric Asset Pricing Modelling
CNAM, Paris, France and INRIA, Grenoble, France
CNAM, Paris, France and CREST, Paris, France
Banque de France, Paris, France and CREST, Paris, France
Address correspondence to Alain Monfort, CREST, Laboratoire de Finance-Assurance, 15 Boulevard Gabriel Peri, 92245 Malakoff, France, or e-mail: monfort{at}ensae.fr
JEL Classification: C1, C5, G12
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Abstract |
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The purpose of this paper is to propose a general econometric approach to no-arbitrage asset pricing modelling based on three main ingredients: (i) the historical discrete-time dynamics of the factor representing the information, (ii) the stochastic discount factor (SDF), and (iii) the discrete-time risk-neutral (RN) factor dynamics. Retaining an exponential-affine specification of the SDF, its modelling is equivalent to the specification of the risk-sensitivity vector and of the short rate, if the latter is neither exogenous nor a known function of the factor. In this general framework, we distinguish three modelling strategies: the direct modelling, the RN constrained direct modelling, and the back modelling. In all the approaches, we study the internal consistency conditions (ICCs), implied by the absence of arbitrage opportunity assumption, and the identification problem. The general modelling strategies are applied to two important domains: security market models and term structure of interest rates models. In these contexts, we stress the usefulness (and we suggest the use) of the RN constrained direct modelling and of the back modelling approaches, both allowing us to conciliate a flexible (non-Car) historical dynamics and a Car (compound autoregressive) RN dynamics leading to explicit or quasi-explicit pricing formulas for various derivative products. Moreover, we highlight the possibility to specify asset pricing models able to accommodate non-Car historical and non-Car RN factor dynamics with tractable pricing formulas. This result is based on the notion of (RN) extended Car process that we introduce in the paper, and which allows us to deal with sophisticated models such as Gaussian and inverse Gaussian GARCH-type models with regime-switching, or Wishart quadratic term structure models.
KEYWORDS: back modelling, Car and extended Car processes, direct modelling, identification problem, internal consistency conditions, Laplace transform, risk-neutral constrained direct modelling
We are grateful to Torben Andersen, Monica Billio, Bjorn Eraker, Marcelo Fernandes, Andras Fulop, René Garcia, Christian Gourieroux, Martino Grasselli, Steve Heston, Nour Meddahi, Patrice Poncet, Ken Singleton, David Veredas, and to seminar participants at CREST Financial Econometrics Seminar 2007, North American Summer Meeting of the Econometric Society 2007 (Fuqua School of Business, Duke University), University Ca' Foscari of Venice 2007, Queen Mary University of London 2008, University of St. Gallen 2008, Université Libre de Bruxelles 2008, ESSEC Business School (Paris) 2008, the Society for Financial Econometrics (SoFiE) Inaugural Conference 2008 (Stern Business School, New York University), Computational and Financial Econometrics Conference 2008 (Neuchatel), Far Eastern and South Asian Meeting of the Econometric Society (FEMES) 2008 (Singapore Management University) for comments. We are especially grateful to Eric Renault (the editor) and an anonymous referee, whose suggestions have helped us to improve this article substantially. Any errors are our own.
Received June 11, 2007; revised May 26, 2008; accepted July 18, 2008