Dependence structure of market states

TL;DR

This paper investigates the dependence structure of market states using empirical pairwise copulas of stock returns, comparing them with a random matrix model, and finds stronger lower tail dependence during crises.

Contribution

It introduces a comparison between empirical copulas of market states and a bivariate K-copula derived from a random matrix model, highlighting dependence asymmetries.

Findings

Good agreement between empirical and analytical copulas, especially for normalized returns.

Detection of asymmetry with stronger lower tail dependence during crises.

Deviations observed in the tails of the copulas.

Abstract

We study the dependence structure of market states by estimating empirical pairwise copulas of daily stock returns. We consider both original returns, which exhibit time-varying trends and volatilities, as well as locally normalized ones, where the non-stationarity has been removed. The empirical pairwise copula for each state is compared with a bivariate K-copula. This copula arises from a recently introduced random matrix model, in which non-stationary correlations between returns are modeled by an ensemble of random matrices. The comparison reveals overall good agreement between empirical and analytical copulas, especially for locally normalized returns. Still, there are some deviations in the tails. Furthermore, we find an asymmetry in the dependence structure of market states. The empirical pairwise copulas exhibit a stronger lower tail dependence, particularly in times of crisis.