Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns

TL;DR

This paper introduces a novel skew-t copula model for financial data that captures asymmetric and tail dependencies more effectively, along with a fast Bayesian inference method, demonstrating improved intraday return modeling and portfolio performance.

Contribution

It proposes a new skew-t copula model with higher asymmetric dependence, and develops a Bayesian variational inference approach for high-dimensional estimation.

Findings

The copula captures significant heterogeneity in asymmetric dependence among equities.

Asymmetric dependencies vary over time and improve predictive density accuracy.

Portfolio strategies based on these dependencies outperform benchmarks.

Abstract

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index.