Chaos-stochastic approaches to market risk.

Summary The complexity of financial markets and the resurgence of particularly severe crises are contributing to the evolution and questioning of so-called standard econometric models for explaining and forecasting financial dynamics. The warning given jointly by prudential managers and researchers aims at encouraging the development of more complex, non-linear models largely inspired by other disciplines. We argue in this thesis that a chaos-stochastic approach to financial chronicles is likely to lead to better results. The relevance of this association is evaluated for market risk in two distinct analytical frameworks. We show the interest of a synthesis of chaotic models and GARCH specifications with or without Markovian regime shifts (MRS) for the modeling and forecasting of the Value-at-Risk of Eurozone stock indices. This study shows better results for the chaos-stochastic models and, in the case of the MRS-GARCH specifications, a better adequacy of the chaotic model of Lasota(1977) for the Southern European indices, which are particularly more volatile than those of Northern Europe for which we recommend the Mackey-Glass(1977) model. This combination allows us, in a bivariate framework, to better understand the links between the different stock markets of the euro zone. We introduce two new specifications that integrate the issues related to correlation breaks: the first one allows us to distinguish, through a sub-period analysis, the interdependence relationships from the contagion phenomena and the second one proposes, in a unified framework, to integrate the correlation breaks. This dual analysis highlights the driving role of the Franco-German index pair, the existence of two distinct spheres made up of Northern European indices on the one hand and Southern European countries on the other, and the intensification of certain relationships between indices following the sovereign debt crisis. We note and insist on the relevance of a chaotic model on average to account for part of the volatility wrongly attributed to GARCH effects.