Generative Models of Multivariate Dependence for Asset Returns

Description

We propose to model tail dependencies separately from correlations motivated by ample empirical evidence of extreme co-movements not captured by the correlation measure. On the methodology side, we construct a new family of heavy-tailed random vectors as known random vectors transformed by a new quantile function. The main contribution of this proposal is the generative model based on transformation by quantile functions, which captures correlations, tail heaviness, and tail dependence by separate parameters. In particular, there are three novelties. First, these generative models are multivariate, which is a significant generalization to earlier work on constructing univariate generative models. Second, they have parameters not only controlling the marginal tail heaviness, but also capturing the pairwise tail dependencies separately from the correlation parameters. This is an essential advantage over existing multivariate models. Third, our model specifications come in two flavors: the lower-triangular model, which is a full version that extends the Gaussian vector factorization case, and the one-factor tail dependence model as a low-dimension special case. Our model has a compact, easy to interpret mathematical form and is generic enough to be applied to non-financial fields, e.g., climatological datasets, where tail dependence is essential. Through preliminary work, we are convinced of the potential of this model. Going forward, we plan to first further investigate the capacities of the proposed model family both theoretically and numerically. We will then study the estimators of these models and examine the efficiency and consistency properties of them. In the end, we will test this model comprehensively on multivariate asset return data in the contexts of financial risk management and empirical asset pricing.