Financial markets are increasingly becoming more interconnected (Moghadam and Vinals 2010), and shocks initially affecting one part of the system can quickly propagate to the rest of it. Therefore, understanding the patterns of distress propagation within financial markets is important to characterize systemic risk. After the global financial crisis of 2007–9, significant effort has been devoted to understanding the mechanics of distress propagation within banking systems. One strand of the literature has focused on modeling the processes through which contagion may occur in interbank networks (see, for example, Glasserman and Young (2016) and Caccioli et al (2018) for recent reviews). Another strand of the literature has focused on the quantification of systemic risk from market data (see Adrian and Brunnermeier 2016; Brownlees and Engle 2016). In particular, Diebold and Yilmaz (2009) proposed a method based on forecast error variance decomposition (FEVD) of estimating from market data networks of interdependencies between firms, and they used the connectedness of the estimated networks to quantify spillovers of uncertainty between variables.

In this paper, we use the methodology of the aforementioned work by Diebold and Yilmaz (2009) to estimate the time evolution of connectedness in three regional banking systems: North America (NA), the European Union (EU) and Southeast Asia (ASEAN). Through VAR and FEVD, we compute the pairwise connectedness between pairs of banks in each region, and we aggregate such pairwise connectedness to compute a measure of total connectedness for the region.

The time-varying total connectedness computed for each banking system, from a 300-day rolling window during the period from January 2005 to October 2015, indicates temporal changes of systemic risk, with peaks during major crisis events and troughs during normal periods. Analogous results have been observed in other financial systems and different regions (Diebold and Yilmaz 2009, 2012, 2014; Chau and Deesomsak 2014; Alter and Beyer 2014; Fengler and Gisler 2015; Demirer et al 2018). It has to be stressed that, unlike Diebold and Yilmaz (2009), who view all financial institutions as belonging to one global system, here we group banks into three regional banking systems. In this way, we can perform a comparative analysis between the different regions, which allows us to highlight similarities and differences between them. Further, this allow us to quantify the existence of causal relations between different regions. Note that combining all the banks together could be somehow misleading, because the banks’ equities in the three banking systems trade in different stock markets that have significantly different trading hours.

The main results of our analysis are as follows. First, we note that the structure of the peaks in the three regional banking systems is very similar, with large peaks associated with significant, identifiable major events. Although the overall patterns are similar, we observe two important differences between the systems. The first is the fact that the overall scale of connectedness is different, with the NA banking system being more interconnected than that in the EU, which, in turn, is more interconnected than the ASEAN system. Second, we uncover the existence of lead–lagged relations between the different time series. To quantify this effect, we compute the transfer entropy between the time series associated with changes of connectedness in the different regions, and we uncover the existence of significant net information flows from NA to the EU, from NA to ASEAN, and from the EU to ASEAN. The robustness of our finding is tested using different measures for transfer entropy. In particular, we find consistent results for the net information flow both with a linear measure of transfer entropy (which corresponds to a Granger causality analysis) and with nonlinear measures of different parameters. We also retrieve similar causal relations for both one-day and five-day returns. To the best of our knowledge, this causality study between regional uncertainties is the first of its kind.

The rest of this paper is organized as follows. In Section 2, we present a literature review and place our paper in the context of previous works. In Section 3, we describe the used data, while Section 4 provides a brief description of our methodology. Section 5 illustrates and discusses the main results of the paper. We present our conclusions in Section 6.

The literature on systemic risk and contagion in the banking network can be broadly classified into two categories. The first category comprises network models that aim to describe various causal mechanics of financial contagion, which can be calibrated with balance-sheet data (Furfine 2003; Degryse and Nguyen 2007; Upper and Worms 2004; Müller 2006; Cont et al 2010; Upper 2011; Birch and Aste 2014). The second category comprises econometric models that aim to identify spillover effects exclusively from market data, without making assumptions about the dynamics of distress propagation between banks (Adrian and Brunnermeier 2016; Brownlees and Engle 2016). Our paper is close to this second strand of the literature, as we try to understand whether market data carries information about the level of interconnectedness between banks and how exogenous shocks can be amplified by the endogenous dynamics of financial markets.

Network models of contagion go back to the seminal work of Allen and Gale (2000), who showed how the stability of the banking system is affected at equilibrium by the pattern of interconnections between banks, and to the work of Eisenberg and Noe (2001), who demonstrated how to consistently compute a clearing vector of payments in a network of interbank claims. The relation between the structure of an interbank network and its stability has also been extensively explored within the context of nonequilibrium network models (see, for example, Furfine 2003; Iori et al 2006; Nier et al 2007; Gai and Kapadia 2010; Cont et al 2010; Upper 2011; Battiston et al 2012; Fricke and Lux 2015; Bardoscia et al 2015, 2017; Kobayashi and Hasui 2014; Lenzu and Tedeschi 2012; Tedeschi et al 2001), showing in particular the existence of a tension between individual risk and systemic risk: what makes a bank individually less risky might in fact increase the risk of a systemic failure (Beale et al 2011). More recently, these analyses have been extended beyond interbank lending networks to the study of networks of overlapping portfolios (Huang et al 2013; Caccioli et al 2014; Corsi et al 2016). Although these models have been insightful with regard to understanding the dynamics of financial contagion, and in some cases they have been applied to real data (see Upper (2011) for a review of the existing literature), there are clear challenges to their applicability. First, there is a lack of reliable data on banks’ balance sheets, which makes it hard to calibrate models.¹¹Admati et al (2013) report that banks tend to find ways to get around regulations in order to invest in mortgage-backed securities and derivatives via structured-investment vehicles, which are off-balance-sheet items. Such leeway being allowed by regulations creates regulatory boundaries, making it difficult for outsiders to know what banks actually report. Second, to obtain a reliable assessment of systemic risk one has to capture all relevant types of interconnections between banks, as the interaction between different contagion channels can significantly change the stability of the system (Caccioli et al 2015).

Here, we take the complementary approach of inferring interdependencies between banks from market data, which belongs to the second strand of literature mentioned above. The advantage of this approach with respect to network modeling is that market data is readily available, and different types of interconnections between banks have already been aggregated by the market. The drawback is that this approach does not provide an explanation of how stress propagates between banks, and it relies on the underlying assumption of market efficiency, which is not realistic (Shiller 2003). Nevertheless, one can assume that, although markets are not efficient, prices do reflect to some extent the aggregate information (or expectations) about the underlying assets. There have been several contributions to this strand of the literature. In particular, Dungey et al (2005) provide a summary of empirical models of contagion up to 2005. More recent empirical work includes Diebold and Yilmaz (2009, 2012, 2014), Caceres et al (2010), Billio et al (2012), Claeys and Vasicek (2014), Lucas et al (2014), Musmeci et al (2015) and Brownlees and Engle (2016). Of particular relevance for our paper is the work of Diebold and Yilmaz (2009, 2012, 2014), which influenced subsequent studies such as McMillan and Speight (2010), Bubák et al (2011), Fujiwara and Takahashi (2012), Klößner and Wagner (2014), Alter and Beyer (2014), Chau and Deesomsak (2014), Demirer et al (2018) and Fengler and Gisler (2015). This strand of contributions uses vector autoregression (VAR) and forecast error variance decomposition (FEVD) to quantify the unpredictability of each variable in the network. By using the VAR and FEVD methods, it is possible to disentangle the contribution to unpredictability due to endogenous interdependencies from that due to exogenous shocks. Following Diebold and Yilmaz, we will refer to this endogenous component in our paper as total network connectedness, which therefore quantifies the transmission of shocks from banks within the system.

We collect daily stock prices from January 2005 to October 2015 of banks headquartered in NA (including the United States and Canada), the EU and ASEAN from the Compustat database. We select only financial institutions in the subindustry “Banks” (ie, large banks operating at the national level and having a GICS code of 40101010) and compute log returns from the daily closing prices for each bank. With the aforementioned criteria, our sample includes ten publicly listed banks in NA, sixty-six banks in the EU and thirty-nine banks in ASEAN that survived through the period January 2005–October 2015.

While we could analyze rolling windows in which the number of banks in operation varies from one window to the next, we find that being able to see the evolution of the systems’ total connectedness given a constant number of banks provides some baseline insight into how the same set of banks reacted to different economic and financial episodes over time. That being said, research that saw all surviving banks being accounted for in respective rolling windows would be an interesting avenue to explore. In such a case, the dimensions of the rolling windows would likely be much larger and estimation techniques such as sparsity modeling would be needed.

All banks in the NA banking system have their stocks traded in the New York Stock Exchange (NYSE), while the EU and ASEAN bank stocks mostly trade in their own national stock markets. Lists of banks in all three regions as well as their summary statistics are given in Tables 1–3.

The data was analyzed over rolling windows of 300 days and over the full period. Harris (1985) recommends using a sample size such that $n\ge 50+k$, where $k$ is the number of predictors. For our study, the minimum number of observations for each rolling window is thus $50+63=113$. We experimented with window sizes of 250, 500 and 750 days and obtained similar results in terms of the overall shape, including peaks and troughs, of total connectedness. We chose the window size of 300 days because it is a good compromise between obtaining results with a reasonable margin of error and making sure we cover the period of interest (March 2006 to November 2015). A window size of 500 days would provide results with a lower margin of error but cover the period from January 2007 onward, while a window size of 250 days would provide results with a higher margin of error but cover the period from January 2006 onward.

We investigate regional and inter-regional uncertainty spillovers in the NA, EU and ASEAN banking systems during a period characterized by great regional and global financial stress (2005–15). Uncertainty and financial instability is quantified by means of total network connectedness, which we measure by improving on the method of Diebold and Yilmaz (2009). We demonstrate that exponential smoothing and ridge regression provide better-defined peaks in the temporal analysis and avoid the occurrence of some spurious peaks. We observe that the NA system appears to be consistently more interconnected than that of the EU, which in turn is more interconnected than the ASEAN network. Similarly to the previous analysis of Diebold and Yilmaz of other systems, our empirical analysis of the NA, EU and ASEAN banking networks shows that increased connectivity corresponds to periods of higher distress in the system. We observe that all large peaks of total network connectedness are associated with identifiable major exogenous events. Despite some of these events being related to specific regions, the effects are seen across all three banking systems, which reveal similar patterns of peaks and troughs in the variations of their total network connectedness. However, such variations are not perfectly synchronous across the regions, and causality patterns are discovered using transfer entropy. Our analysis reveals that the NA banking system is the most influential, having the largest effect on the other systems. However, feedback effects are measured with significant causal relations in the opposite direction as well. The results are demonstrated to be robust with respect to changes in the method used to compute the transfer entropy, changes in the values of parameters, and with respect to the use of daily or weekly returns in the analysis.

To summarize, the contribution of this paper is threefold. First, we improve the technical aspect of VAR estimation, allowing for better identification of events concentrated at specific times, which leads to a more accurate and insightful interpretation of the results. Second, we focus on connectedness in the banking sector, while previous studies based on the Diebold and Yilmaz (2009) methodology have analyzed networks of financial institutions. In particular, we analyze the NA, EU and ASEAN banking systems individually and show that, despite the regions’ being geographically distant, they are affected to varying degrees by major financial crisis events originating in dominant regions such as the NA and EU banking systems. Third, we perform a causality analysis on the regional connectedness time series generated using Diebold and Yilmaz’s method. Our analysis suggests that a regional disaggregated investigation has the advantage of introducing a predictive component to this methodology. While the network total connectedness measure identifies increases in regional uncertainty associated with major events that shake the markets, the causality relation between total connectedness in different regions – introduced in this paper – provides a quantitative characterization of the flow of uncertainty from region to region, which could be interpreted as the result of contagion. To the best of our knowledge, this causality analysis is the first of its kind.

In future, we will compare this approach with other information theoretic measures with the aim of finding a framework that is capable of qualifying financial uncertainty and its causal effects at all levels of aggregation, from a local single-variable perspective to a global world-market view.

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

T.A. and F.C. acknowledge the support of the UK Economic and Social Research Council (ESRC) in funding the Systemic Risk Centre (ES/K002309/1).