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«SYRTO WORKING PAPER SERIES Working paper n. 16 | 2015 This project has received funding from the European Union’s Seventh Framework Programme for ...»

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Coupling direction of the

European banking and

insurance sectors using

inter-system recurrence


Peter Martey Addo


Working paper n. 16 | 2015

This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and

demonstration under grant agreement n° 320270.

This documents reflects only the author's view. The European Union is not liable for any use that may be made of the information contained therein.

Coupling direction of the European Banking and Insurance sectors using inter-system recurrence networks *Preliminary and Incomplete. Please do not QUOTE. * Peter Martey ADDOa,b,∗ a Centre National de la Recherche Scientifique (CNRS), France ´ b Centre d’Economie de la Sorbonne (CES) - CNRS : UMR8174 - Universit´ Paris I - e Panth´on Sorbonne, France e Abstract Modern financial systems exhibit a high degree of interdependence making it difficult in predicting. This has raise concerns on the correct identification of coupling direction in financial sectors of the economy. This study explores a “two–way” risk connection between the European banking and insurance sector based on geometrical closeness of observations. Specifically, the study looks at the inter-system recurrence networks in tracing dynamical transi- tions and detecting coupling direction between these sectors. The overall results shows that the banking sector is central in risk transmission com- pared to the insurance sector. A comprehensive discussion of the feasibility and relevance of the approach in studying systemic risk is provided.

Keywords: Financial institutions, Recurrence networks, Systemic risk, Recurrence plots ∗ The author gratefully acknowledge funding from the European Union’s Seventh Framework Programme (FP7-SSH/20072013) for research, technological development and demonstration under grant agreement no 320270 (SYRTO).

Email address: peter.addo@univ-paris1.fr (Peter Martey ADDO) Preprint submitted to Elsevier June 17, 2015 JEL: C40, E50, G01, G20

1. Introduction The threat of systemic risk to the financial system has drawn attention to research on uncovering dependencies among financial sectors, institutions, and economic regions/cross-borders (Hartmann et al. (2005); Cummins and Weiss (2014)). Large bank failures and insurer distress due to the recent global financial crisis have raise concerns on the proper identification of cou- pling direction between the banking and insurance sectors. Identifying sys- temic linkages through the financial sectors of the economy is relevant in understanding risk transmissions to enhance policymaking. The convergence of financial activities in the banking and insurance sectors has raised macroprudential concerns on the interconnectedness and systemic dependencies between these sectors to enhance proper monitoring. In other words, the identification of sources of systemic risk is of crucial importance to regulators for proper control.

Recent works documented in literature on systemic dependencies include Billio et al. (2012); Slijkerman et al. (2013); Cummins and Weiss (2014), among others. Most of the approaches are focused on quantification of temporal interrelationships of observations such as correlation methods, conditional mutual information methods (Addo et al. (2015)), and autoregressive models. The question that arises is whether structural characterisation based on geometrical closeness of observations provide insights to uncovering transitions and causal interdependencies. In this work, we consider the intersystem recurrence networks based on geometrical considerations to analyse 2 systemic dependence in the financial sector.

The study examines systemic dependence between bank and insurance sectors of the financial sector to uncover the sector that poses a higher systemic threat to financial stability. We investigate these risk transmission considering the period prior to the global financial crisis, during the crisis, and post-crisis period. In particular, we study how these risk transmissions change over time and under different economic conditions. Uncovering coupling direction between these sectors is very relevant for the introduction of some regulatory measures to enhance financial stability. We claim that the identification of such coupling direction is crucial in identifying sources of instabilities or potential risks in the financial system. Overall, our findings points that risk transmissions have mainly been from the banking sector to the insurance sector and not the vice versa. To the best of our knowledge, this work marks the first application of inter-system recurrence networks in economics and finance.

The structure of the remainder of this paper is as follows. Section 2.1 presents a description of the considered datasets used in studying the coupling direction. Section 2.2 presents an overview of inter-system recurrence networks and it’s associated complex network measures useful in studying nonlinear dynamics of underlying time series data. Section 2.3 provides information on available programming packages for the implementation of the method. The empirical application of the method to studying the dynamics and coupling direction prior and during the global financial crisis and the European Sovereign debt crisis is then provided. Finally, in Section 3, we discuss the results and provide concluding remarks on the advantages of this

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2. Data & Method

2.1. Data description The data used in our empirical analysis consist of daily EMU (European Economic and Monetary Union) MSCI Bank sector equity total return index and Insurance sector equity total return index over the period (29/12/2000– 23/04/2015). The start date of the sample is chosen in order to study coupling direction dynamics prior and during the global financial crisis and the European Sovereign debt crisis. Our daily data are sourced from Macrobond database.

Figure 1: Daily EMU (European Economic and Monetary Union) MSCI Bank sector equity total return index and Insurance sector equity total return index over the period (29/12/2000–23/04/2015).


2.2. Inter-System Recurrence Network & Measures for Coupling direction Recurrence network analysis has been successfully used in tracing dynamical transition in non-stationary time series based on mutual proximity of state vectors (observations) in phase space (Marwan et al. (2009); Donner et al. (2010b, 2011b)). Recurrence networks make use of the geometrical closeness in phase space via recurrence structure of the underlying time series by representating these structures as a connectivity pattern of an associated complex network (Donner et al. (2011a); Donges et al. (2012)). Let {bi }Nb i=1 and {sj }Ns represent realisations of banking sector B and insurance sector S j=1 recorded at times ti (i = 1, 2, · · ·, Nb ) and tj (j = 1, 2, · · ·, Ns ), respectively.

Here bi = B(ti ) and si = S(tj ). The recurrence matrix associated with the banking sector (similarly the insurance sector) is given by

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where · denotes a suitable distance norm (i.e. say the supremum norm), and Θ(·) is the Heaviside function. The threshold ε· for the recurrence anal ysis is chosen to be equal to σ m/10, where σ is the fluctuation level in signal, m is the embedding dimension of the signal (Letellier (2006)). This choice of ε· is such that the value corresponds to 10% of the maximum phase space diameter or such that the recurrence rate is 10% (Schinkel et al. (2008);

Thiel et al. (2002); Marwan et al. (2007)). Measures based on the emergence of line structures of the plot of the recurrence matrix (1) are known as recurrence quantification analysis (RQA) Zbilut and Webber (1992); Marwan and 5 Kurths (2002); Marwan et al. (2007). These measures are useful in characterising the dynamics and tracing transitions in the underlying time series.

The concept of recurrence plots have been extended to complex network perspective by defining an adjacency matrix associated with equation (1) as

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where δi,j denote Kronecker’s delta (δi,j = 1 if i = j, otherwise δi,j = 0).

The adjacency matric can be viewed as the recurrence matrix with self-loops removed. The equation (3) defines the recurrence network of an underlying data (Marwan et al. (2009); Donner et al. (2010b, 2011b)). These networks have been successfully used in the identification of dynamical transitions in marine palaeoclimate records (Donges et al. (2011)). The first application of recurrence networks and its associated network measures in economics was in Addo (2015). The feasibility of this network approach in studying spatial dependencies, and tracing dynamic transitions in sovereign credit default swaps and government bond yields prior and during the European debt crisis was introduced in Addo (2015). In this work, we focus on an inter-sectoral analysis by the means of inter-system recurrence networks as a new extension to the application of recurrence networks in economics.

Using the definition of cross-recurrence matrix (2) and recurrence network (3), the inter-system recurrence network is defined by

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7 be useful in identifying coupling direction between the banking sector and insurance sector. In Table (2), the expected signatures of inter-system recurrence network measures in different coupling situation is provided (Feldhoff et al. (2012); Donges et al. (2012)). The coupling directions are based on the definitions of global cross-clustering coefficient and cross-transitivity coefficient presented in Table (1). In general, the transitivity coefficient is a more robust measure than the global clustering coefficient especially in short time series (Newman (2002); Saramaki et al. (2007); Donner et al. (2010b);

Donges et al. (2011)).

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2.3. Implementation In the implementation of the recurrence networks and calculation of complex network measures, we make use of the Python programming language, and in particular the package “pyunicorn”. The Python packages

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Table 2: Signatures of Coupling based on the global cross-clustering coefficient and crosstransitivity recurrence network measures. T SB and C SB denotes the cross transitivity and global cross-clustering coefficient of S with respect to B respectively. The unidirectional coupling is denoted by the arrow “−→”, whilst the arrow “←→” denotes a bidirectional coupling. See Donges et al. (2012); Feldhoff et al. (2012) for a detailed discussion.

“NetworkX” and “PyGraphviz” have been used for the visualization of network graphs. Following Addo (2015), we make use of the Los Alamos National Laboratory (lanl) internet routes algorithm for the graphical representation of the complex networks based on the adjacency matrices.

In the section that follows, we will present the results on detecting coupling directions in banking and insurance sectors by means of inter-system recurrence networks described in Section (2.2). A discussion of the feasibility and relevance of the approach in studying “two–way” (bivariate) risk connections among sectors is then presented.

3. Discussion of Results & Concluding Remarks In this section, we present results on the empirical application of intersystem recurrence networks in detecting coupling direction between two sectors of the European financial sector. Figure 1 shows the plot of the daily 9 EMU MSCI Bank sector equity total return index and Insurance sector equity total return index over the period (29/12/2000–23/04/2015). In general, the banking sector returns were relatively higher compared to the insurers especially between year 2003–2009. From this figure, it is evident that the banking sector was strongly hit during the recent global financial crisis. This could be due to risk exposures arising from banking operations on the interbank market and banking assets. The recurrence plots associated with the banking and insurance sectors are displayed in Figure 2a and Figure 2b respectively. We refer to these plots as the “intra-sectoral” recurrence plots.

The butterfly-like structures on the diagonal of the recurrence plots in Figure 2 mark times of distress in these financial sectors of the economy (Addo et al. (2013)). Figure 3 shows the cross recurrence plot for the sectors and the graphical representation of the inter-sector recurrence network. The cross recurrence plot displays times that observations in both sectors simultaneously recur. The recurrence plot of the inter-sector recurrence matrix is provided in Figure 4a and the associated degree rank plot in Figure 4b. The recurrence network measures in Table 3 indicates the presence of assortativity patterns with variations in the average path length implying dynamic transitions in the financial system. The results on the coupling direction for the banking and insurance sector across time is presented in Table 4. Overall, we find a coupling direction from the banking sector to the insurance sector which implies the direction of risk transmission between these sectors.

The correct identification of coupling direction in financial sectors of the economy is one of the main challenges in studying in the high degree of interdependence in the financial system. In this paper, we consider a structural 10 (a) Bank Sector Recurrence Plot (b) Insurance Sector Recurrence Plot Figure 2: The recurrence plot of the adjacency matrices of the recurrence network associated with the Banking and Insurance Sectors respectively over period 29/12/2000– 23/04/2015. This can also be referred to as the “intra-sectoral” recurrence plots. The time indexes corresponds to the following calender dates: “500”= 11/28/2002, “1000” = 10/28/2004, “1500”= 9/28/2006, “2000”= 8/28/2008, “2500”= 7/29/2010, “3000”= 6/28/2012, “3500”= 5/29/2014.

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