Resilience for financial networks under a multivariate GARCH model of stock index returns with multiple regimes

Abstract

Targeting systemic risk, we propose a two-stage analysis of a large collection of stock markets by considering their interconnections. First, we characterize the joint dynamics of stock returns using a multivariate GARCH model in the presence of regime changes. The model detects three regimes of volatility rising from two unknown but common endogenous breaks. We compute filtered returns by normalizing them using the dynamic GARCH volatility. Second, we build a Gaussian signed weighted and undirected worldwide financial network from filtered stock returns, that evolves across regimes. The best network is built from the partial correlation matrix of filtered stock returns over each regime using regularisation and the minimum Extended Bayesian Information Criterion. To gain insights into the resilience of the financial network and its systemic risk over time, we then compute relevant nodal centrality measures—including the clustering coefficient—over each regime. Thus, we characterize the ever-changing network topology and structure by detecting group-like and community-like patterns (e.g., clustering and community detection, network cohesion). Under the resilience framework and depending on the studied regime, we analyse the propensity of a shock to propagate across the network thanks to positive weights, and the network’s ability to mitigate shocks thanks to negative weights. The balance between spreading and inhibiting node influences drives the network’s frailty and resilience to shocks. Hence, the network exhibits a high level of systemic risk when its connectivity is large and most edge weights are significantly positive (i.e., strong and multiple conditional dependencies of world stock markets). It is of high significance to policymakers because systemic risk/financial frailty is potentially costly (i.e., loss) while resilience is rewarding (i.e., gain).

Appendix: Daily GARCH estimates

From the 3rd January 2000 to the 8th July 2022, the daily sample size is T = 5875 (observations per series). The region-specific daily results are displayed in the forthcoming tables as follows. Table

Table 9 Regional multivariate GARCH(1,1) changepoints

9 displays the estimated changepoints (i.e., break dates) for each region, while Tables 

Table 10 Regime-specific estimates of DCC GARCH(1,1) parameters for America

10,

Table 11 Regime-specific estimates of DCC GARCH(1,1) parameters for Europe

11 and

Table 12 Regime-specific estimates of DCC GARCH(1,1) parameters for Asia

12 present the estimated GARCH(1,1) parameters across regimes and for each region on a daily basis. We find different regimes for stock returns across regional marketplaces.

See Tables 9, 10, 11 and 12

In America, stock market indices exhibit (strong) persistence in volatility over time except for IPC index during period 3. Correlations persist over all periods except period 3. In Europe, individual volatilities of indices are strongly persisting across periods except for the following cases. CACALL index exhibits weak volatility persistence over period 2, while DAX, SMI, AEX, IBEX35, and OMXS indices exhibit small volatility persistence over period 3. Periods 1 and 2 exhibit almost no correlation persistence, while a low correlation persistence arises over period 3, giving then rise to strongly persisting correlations from period 4 to period 6. In Asia, stock market indices globally exhibit small persistence in volatility over periods 1, 2 and 5, while volatilities exhibit strong persistence over remaining periods 3, 4, 6, 7 and 8. Periods 1, 2 and 5 exhibit a small persistence in correlations, while the remaining periods 3, 4, 6, 7 and 8 strong exhibit persistence in correlations.

1.1 Clustering coefficient for signed networks

We apply the extension proposed by Costantini and Perugini (2014). The corresponding clustering coefficients per regime are displayed in the table below.

See Table 

Table 13 Extension of Onnela et al. (2005) clustering coefficients to signed networks

13

Obviously, considering weights' signs yields narrower standardized clustering coefficients because of the interplay between negative and positive node influences. Indeed, positive edges illustrate amplifying connections (e.g., risk frailty) within the network, and interact with negative edges that reflect inhibiting connections (e.g., risk resistance). Such interplay balances the network (shock spreading versus shock mitigation).