Une nouvelle formalisation de la dynamique du système des prix du marché action (A New Formalization of the Dynamics of the Market Price System of the Equity Market)

Abstract

French abstract: Le present papier formalise un nouveau modele de dynamique du systeme des prix du marche action, capable de saisir un large spectre de phenomenes renseignes par la litterature academique financiere. Le modele s’attache particulierement a rendre compte de trois faits empiriques majeurs, generalement absents des macro-modeles financiers : les queues de distribution paretiennes des rendements, la propension du marche a la poursuite de tendances, et le changement de regime de volatilites lors des periodes de materialisation du risque systemique. Prenant comme point de depart la relation du CAPM adaptee a une approche factorielle, le modele incorpore ensuite l’effet momentum, pour le consacrer comme phenomene financier de premiere importance. Sur la base de donnees empiriques, une theorie de la dynamique des variances factorielles est ensuite introduite, theorie dans laquelle les valeurs d’attraction des variances dependent d’un parametre de tendance du portefeuille de marche. L’articulation de cette theorie avec l’effet momentum permet de deduire un modele de krachs boursiers semi-endogenes, evenements durant lesquels les relations de dependances entre actifs se voient profondement modifiees. Un compte-rendu des resultats obtenus a l’issue d’une serie de simulations basees sur le modele propose vient enfin cloturer ce papier. English abstract: The present paper formalizes a new model of the dynamics of the stock market price system, able of capturing a wide spectrum of phenomena informed by the financial academic literature. The model particularly accounting three major empirical facts generally absent from financial macro-models: the Paretian distribution tails of returns, the market's propensity to pursue trends, and the change in the volatility regime during periods of systemic risk materialization. Taking as a starting point the relation of the CAPM adapted to a factorial approach, the model then incorporates the momentum effect, to establish it as a major financial phenomenon. Based on empirical data, a theory of the dynamics of factorial variances is then introduced, in which the attraction values of the variances depend on a trend parameter of the market portfolio. The articulation of this theory with the momentum effect makes it possible to deduce a model of semi-endogenous stock market crashes, events during which the relationships of dependence between assets are profoundly modified. A report on the results obtained from a series of simulations based on the proposed model finally concludes this paper.