Interconnected multilayer networks: Quantifying connectedness among global stock and foreign exchange markets

Highlights

• Interconnected multilayer networks linking 40 stock markets and 30 forex markets are built.

• Stock markets transmit the largest spillovers to forex markets.

• The French stock market is the largest risk transmitter in multilayer networks.

• Most Asian stock markets and forex markets serve as net risk receivers.

• Cross-market and within-market spillovers show different behaviors during GFC and COVID-19.

Abstract

This paper proposes a novel interconnected multilayer network framework based on variance decomposition and block aggregation technique, which can be further served as a tool of linking and measuring cross-market and within-market contagion. We apply it to quantifying connectedness among global stock and foreign exchange (forex) markets, and demonstrate that measuring volatility spillovers of both stock and forex markets simultaneously could support a more comprehensive view for financial risk contagion. We find that (i) stock markets transmit the larger spillovers to forex markets, (ii) the French stock market is the largest risk transmitter in multilayer networks, while some Asian stock markets and most forex markets are net risk receivers, and (iii) interconnected multilayer networks could signal the financial instability during the global financial crisis and the COVID-19 crisis. Our work provides a new perspective and method for studying the cross-market risk contagion.

Introduction

Connectedness is a crucial concept in financial markets and has a significant impact on the stability of financial system. The linkages between entities (e.g., financial markets and financial institutions) in the financial system are usually complex and multidimensional. The forex market is the world’s largest financial market with an enormous transactions and strong liquidity, and its volatility has broad implications on imports and exports, commodity prices, capital flows, economic output and employment. The stock market is also important since it has a direct relationship with the economy and trade activities. According to the triennial central bank survey of Bank for International Settlements, the global forex market traded at high levels, with an average daily trading volume rising to $7.5 trillion in April 2022.¹ At the end of June 2022, the market capitalization of U.S. stock markets reached approximately $43 trillion. The increasing transactions between financial markets in different areas would increase the independency as well as volatility spillovers in the financial system. Especially, the comovement and risk contagion among different financial markets would increase when facing new crises and uncertainties (e.g., the COVID-19 pandemic and the geopolitical conflict).²

Although the connectedness between stock and forex markets has been thoroughly researched, most of the existing literature generally examines risk contagion or volatility spillovers between a few developed and developing markets separately, or between some organizations such as the G7 and BRICS (Beer et al., 2008, Erdoğan et al., 2020, Grobys, 2015, Morales, 2008, Morales-Zumaquero and Sosvilla-Rivero, 2018, Sui and Sun, 2016, Warshaw, 2020, Yang and Chang, 2008, Yang and Doong, 2004). Namely, the global linkages between stock and forex markets are rarely explored at a holistic level (i.e., a network level); in particular, which markets act as a bridge for cross-market risk contagion? Which markets are more important? And how does the structure of financial networks change during catastrophic events? Thus, our goal here is to study cross-market risk contagion among global stock and forex markets from a network analysis perspective, especially, a multilayer network analysis perspective.

Recently, the COVID-19 pandemic has a visibly disruptive impact on the global economy and this impact is being felt. Forex rates in major emerging markets (e.g., Brazil, Mexico, Russian Federation, and South Africa) declined significantly in March 2020, while those in developed economies (e.g., the USA) generally strengthened, which are consistent with previous crises (OECD, 2020). Corsetti and Marin (2020) mention that global financial shocks in 2020 are very different from the 2008 global financial crisis (GFC). Investors quickly withdrew massive capital from emerging markets, which had never been seen before. Global events are bound to affect diverse financial markets in many regions simultaneously. Thus, we also aim to examine cross-market risk contagion among global stock and forex markets during two significant global events (i.e., GFC and COVID-19) using multilayer networks.

Previous research adopts spillover index based framework to explore volatility connectedness in the following two aspects. One concentrates on volatility spillovers in single financial market, such as stock markets (BenSaïda, 2019, McIver and Kang, 2020), forex markets (Wen & Wang, 2020), the banking system (Alter & Beyer, 2014), and cryptocurrency markets (Yi, Xu, & Wang, 2018); and the other focuses on volatility spillovers among multiple financial markets, e.g., stock markets and forex markets (Fernández-Rodríguez and Sosvilla-Rivero, 2020, Grobys, 2015), stock markets and energy markets (Elsayed et al., 2020, Zhang, 2017), and other multiple types of financial markets (Kang et al., 2017, Maghyereh et al., 2016, Malik and Umar, 2019, Reboredo et al., 2021).

The network analysis is an effective method to analyze and quantify the structural characteristics and evolution behavior of financial system. Currently, single-layer financial networks studying risk contagion can be broadly classified into three types of networks: physical network (Brunetti et al., 2019, Fricke and Lux, 2015), correlation network (Boginski et al., 2005, Lyócsa et al., 2012, Mantegna, 1999, Tumminello et al., 2005, Wang et al., 2018), and information spillover network (Billio et al., 2012, Diebold and Yilmaz, 2014, Wang et al., 2017). In contrast to Billio et al. (2012) and Wang et al. (2017) who propose the Granger causality networks (i.e., unweighted spillover networks), Diebold and Yilmaz (2014) construct volatility spillover network based on the spillover index approach considering not only the spillover direction between entities but also the strength of each edge. Nevertheless, the above Granger causality networks and volatility spillover networks fall into the category of single-layer network. Structural limitations make them difficult to describe connectedness across multiple levels, ignoring some important cross-market linkages. Such simplification obviously does not reflect complex scenes in the real world. Thus, the traditional single-layer network has knowledge gap in information spillovers across multiple financial markets. Naturally, we turn to multi-dimensional networks, i.e., multilayer networks.

The rapid development of multilayer network method provides an application opportunity to analyze the multiple connectedness of financial entities. Multilayer networks are a novel and powerful tool for describing, comparing and analyzing various types of financial risk patterns. Multilayer networks are a powerful tool for describing complex systems, reflecting multiple types of associations and interactions. An intuitive explanation of the difference between single-layer network and multilayer networks is that the latter can build the connections between different layers (relationships). According to Boccaletti et al. (2014) and Kivelä et al. (2014), multilayer networks are a collection of different layers connected by interlayer edges, where a specific relationship or activity represents a layer, and the entity may have different kinds of connections, such as interlayer connections and intralayer connections. Nowadays, multilayer networks have emerged prominently in several fields due to their rich structural implications, e.g., multiplex transportation networks (Chodrow et al., 2016, Strano et al., 2015), multilayer social networks (Barrett et al., 2012, Smith-Aguilar et al., 2019, Szell et al., 2010), multilayer biogenetic networks (Li, Liu, Zhang, Waterman, & Zhou, 2011), multilayer epidemic spreading networks (Wei et al., 2018, Zhang and Yang, 2021), and multilayer financial networks applied in stock markets (Wang, Chen, Si, Xie, & Chevallier, 2021), derivatives markets (Abad et al., 2016, Bardoscia et al., 2019), commodity markets (de Jeude, Aste, & Caldarelli, 2019), and interbank markets (Bargigli et al., 2015, Leventides et al., 2019).

In contrast to the single-layer network, the topological characteristics of multilayer networks are calculated differently and mathematically expressed due to their interlayer structures (Kivelä et al., 2014). Multilayer networks can be broadly classified into two types: multiplex networks and interconnected multilayer networks (Finn, Silk, Porter, & Pinter-Wollman, 2019). Multiplex networks are generally set to have the same node set at each layer, and interlayer edges connecting these same nodes at different layers. In the interconnected multilayer network, on the other hand, the settings of node sets in different network layers can be different, and the interlayer edges can exist at different nodes in different layers.

Although multiplex networks have been more frequently applied to analyze risk contagion, most of the literature has not considered the significance of interlayer connections due to the difficulty in obtaining the cross-market data. We notice that interconnected multilayer networks, coinciding with the concept of financial risk contagion across markets, are a natural tool to analyze complex financial system. Therefore, we propose a novel type of interconnected multilayer networks to investigate the within-market and cross-market volatility spillovers among stock and forex markets by combining the spillover index approach and the block aggregation spillover approach. In details, the proposed interconnected multilayer networks connect stock and forex markets from 40 economies in the world, consisting of stock market layer, forex market layer, and the interlayer linking stock and forex markets, which provide a new perspective for cross-market risk contagion analysis. Our study addresses the lacuna that multilayer financial networks only consider intralayer linkages and neglect interlayer edges with extensive implications, and reflects the usefulness of multilayer networks as an analytical tool for cross-market spillovers.

The main contribution of this paper is firstly to propose the interconnected multilayer network framework to study cross-market volatility spillovers among stock and forex markets, facilitating an intensive understanding of how connectedness between markets varies with shocks. Secondly, we compare and analyze the similarities and differences between single-layer networks and multilayer networks to explore the volatility connectedness between stock and forex markets. Finally, we compare the structure of interconnected multilayer networks before and after/during the global financial crisis and the COVID-19 crisis and assess the diverse impact of these crises on financial markets. The network analysis is able to identify crucial nodes and important linkages between global stock and forex markets, which help risk managers make appropriate responses in crises.

The remainder of the paper is organized as follows. In Section 2, we introduce the connectedness measurement, network construction, and versatility measures. In Section 3, we present the data and descriptive statistics. In Section 4, we analyze the empirical results. In Section 5, we draw conclusions.