Graphical copula GARCH modeling with dynamic conditional dependence

TL;DR

This paper introduces the GC-GARCH model, which captures nonlinear tail dependencies in large portfolios using graphical copulas and dynamic structures, improving risk prediction and portfolio returns.

Contribution

The paper develops a novel graphical copula GARCH framework that models complex tail dependencies with a DAG structure and time-varying parameters, enhancing portfolio risk modeling.

Findings

More accurate conditional value-at-risk predictions.

Higher cumulative portfolio returns compared to DCC-GARCH.

Effective estimation of DAG structures in simulations.

Abstract

Modeling returns on large portfolios is a challenging problem as the number of parameters in the covariance matrix grows as the square of the size of the portfolio. Traditional correlation models, for example, the dynamic conditional correlation (DCC)-GARCH model, often ignore the nonlinear dependencies in the tail of the return distribution. In this paper, we aim to develop a framework to model the nonlinear dependencies dynamically, namely the graphical copula GARCH (GC-GARCH) model. Motivated from the capital asset pricing model, to allow modeling of large portfolios, the number of parameters can be greatly reduced by introducing conditional independence among stocks given some risk factors. The joint distribution of the risk factors is factorized using a directed acyclic graph (DAG) with pair-copula construction (PCC) to enhance the modeling of the tails of the return distribution while offering the flexibility of having complex dependent structures. The DAG induces topological orders to the risk factors, which can be regarded as a list of directions of the flow of information. The conditional distributions among stock returns are also modeled using PCC. Dynamic conditional dependence structures are incorporated to allow the parameters in the copulas to be time-varying. Three-stage estimation is used to estimate parameters in the marginal distributions, the risk factor copulas, and the stock copulas. The simulation study shows that the proposed estimation procedure can estimate the parameters and the underlying DAG structure accurately. In the investment experiment of the empirical study, we demonstrate that the GC-GARCH model produces more precise conditional value-at-risk prediction and considerably higher cumulative portfolio returns than the DCC-GARCH model.