Dependence Modeling of Joint Extremes Via Copulas: A Dynamic Portfolio Allocation Perspective

Abstract

Recent empirical evidence highlights the importance of asymmetries in the distribution of asset returns in both their marginal behavior in terms of skewness and their dependence structure in that assets tend to be more highly correlated during bear markets than during market upturns. In this paper we develop a model that is able to address both features of the data based on the construction of a multivariate diffusion with pre-specified stationary distribution using copula functions. The asymmetric tail dependence is captured by a mixture copula of the Elliptic and the Extreme Value families, which is isolated from the marginal behavior, modeled by the flexible Generalized Hyperbolic class of distributions that allows accounting for stylized properties of the data. We further study the effect of asymptotic extreme value dependence on portfolio choice in a complete market setup where optimal allocation rules are obtained analytically under the Martingale technique using Malliavin calculus. We compare the evolution of the intertemporal hedging terms over time induced by a data generating process that allows for asymmetric dependence in the extremes to those of an asymptotically independent model. We assess the importance of the differences in portfolio shares through the certainty equivalent cost of ignoring extreme value dependence and find that taking it into account leads to significant economic gains.