We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systemic factors and random recoveries. As a significant improvement with respect to the literature, we detail all...

We develop a new method for generating dynamics of conditional correlation matrices between asset returns. These correlation matrices will be parameterized by a subset of their partial correlations,whose structure will be described by an undirected graph called 'vine.' Since such partial...

In this paper we discuss some statistical pitfalls that may occur in modeling cross-dependences with copulas in financial applications. In particular we focus on issues arising in the estimation and the empirical choice of copulas as well as in the design of time-dependent copulas