Dependence calibration and portfolio fit with factor-based subordinators

The paper explores the properties of a class of multivariate Lévy processes used for asset returns. We focus on describing both linear and non-linear dependence in an economic sensible and empirically appropriate way. The processes are subordinated Brownian motions. The subordinator has a common and an idiosyncratic component, to reflect the properties of trade, which it represents. A calibration to a portfolio of 10 US stock indices returns over the period 2009–2013 shows that the hyperbolic specification has a very good fit to marginal distributions, to the overall correlation matrix and to the return distribution of both long-only and long-short random portfolios, which also incorporate nonlinear dependence. Their tail behaviour is also well captured by the variance gamma specification. The main message is not only the goodness of fit, but also the flexibility in capturing dependence and the ease of calibration on large sets of returns.