Dependence Calibration and Portfolio Fit with Factor-based Time Changes

The paper explores the fit properties of a class of multivariate Lévy processes, which are characterized as time-changed correlated Brownian motions. The time-change has a common and an idiosyncratic component, to reflect the properties of trade, which it represents. The resulting process may provide Variance-Gamma, Normal-Inverse-Gaussian or Generalized-Hyperbolic margins. A non-pairwise calibration to a portfolio of ten US daily stock returns over the period 2009-2013 shows that fit of the Hyperbolic specification is very good, in terms of marginal distributions and overall correlation matrix. It succeeds in explaining the return distribution of both long-only and long-short random portfolios better than competing models do. Their tail behavior is very well captured also by the Variance-Gamma specification