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

ArXiv ID: 2308.05564 “View on arXiv”

Authors: Unknown

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.

Keywords: Skew-t Copula, Bayesian Inference, Variational Inference, Tail Dependence, Factor Models

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper presents advanced variational inference methods for a complex Bayesian skew-t copula model with generative representations and variational optimization, requiring substantial mathematical derivation. It provides empirical validation through backtests on high-frequency intraday equity returns across 93 stocks over 5 years, with portfolio selection strategies showing improved performance relative to benchmarks.

  flowchart TD
    A["Research Goal:<br>Model Asymmetric Dependence<br>in Intraday Equity Returns"] --> B["Data Input:<br>93 U.S. Equities<br>(2017-2021 Intraday Returns)"]
    B --> C["Methodology:<br>Skew-t Copula Factor Model<br>with Bayesian VI"]
    C --> D["Computational Process:<br>Stochastic Gradient Ascent<br>to Optimize Variational Posterior"]
    D --> E["Key Findings:<br>1. Captures Heterogeneous Asymmetric Dependence<br>2. Superior Predictive Densities<br>3. Improved Portfolio Selection"]
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style E fill:#ccf,stroke:#333,stroke-width:2px