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Econometric Asset Pricing Modelling

  • Henri Bertholon

    (Crest)

  • Alain Monfort

    (Crest)

  • Fulvio Pegoraro

    (Crest)

The purpose of this paper is to propose a general econometric approach to asset pricing modelling based onthree 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 (R.N.) factor dynamics. Retaining anexponential-affine specification of the SDF, its modelling is equivalent to the specification of the factor loading vectorand 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 Risk-Neutral Constrained Direct Modelling andthe Back Modelling. In all the approaches we study the internal consistency constraints, implied by the absence ofarbitrage opportunity (AAO) assumption, and the identification problem. We also propose interpretations of thefactor loading vector in terms of market price of risk. The general modelling strategies are applied to two importantcases: security market models and term structure of interest rates models. In the context of security market models,we show the relevance of our methods for various kinds of specifications: switching regime models, stochastic volatilitymodels, Gaussian and Inverse Gaussian GARCH-type models (with or without regime-switching). In the interestrates modelling context, we consider several illustrations: VAR modelling, Switching VAR modelling and Wishartmodelling. We also propose, using a Gaussian VAR(1) approach, an example of joint modelling of geometric returns,dividends and short rate. In these contexts we stress the usefulness of the Risk-Neutral Constrained Direct Modellingapproach and of the Back Modelling approach, both allowing to conciliate a flexible historical dynamics and a CarR.N. dynamics leading to explicit or quasi explicit pricing formulas for various derivative products. Moreover, wehighlight the possibility to specify asset pricing models able to accommodate non-affine historical and R.N. factordynamics with tractable pricing formulas. In this respect we introduce the new notion of Extended Car process whichis particularly promising.

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2007-18.

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Length: 45
Date of creation: 2007
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Handle: RePEc:crs:wpaper:2007-18
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