Volatility connectedness in global foreign exchange markets

Journal Pre-proof Volatility Connectedness in Global Foreign Exchange Markets Tiange Wen, Gang-Jin Wang

PII:

S1042-444X(20)30006-2

DOI:

https://doi.org/10.1016/j.mulfin.2020.100617

Reference:

MULFIN 100617

To appear in:

Journal of Multinational Financial Management

Received Date:

15 August 2019

Revised Date:

29 January 2020

Accepted Date:

30 January 2020

Please cite this article as: Tiange Wen, Gang-Jin Wang, Volatility Connectedness in Global Foreign Exchange Markets, (2020), doi: https://doi.org/10.1016/j.mulfin.2020.100617

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Journal of Multinational Financial Management Volatility Connectedness in Global Foreign Exchange Markets --Manuscript Draft-MULFIN_2019_209R1

Article Type:

Research Paper

Keywords:

Currency; volatility spillover; volatility connectedness; financial network; forex markets

Corresponding Author:

Gang-Jin Wang Business School, Hunan University Changsha, Hunan China

First Author:

Tiange Wen

Order of Authors:

Tiange Wen

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Manuscript Number:

Gang-Jin Wang, Ph.D.

We statically and dynamically measure total and directional volatility connectedness in global foreign exchange (forex) markets. We use the volatility spillover index and LASSO-VAR approaches in the variance decomposition framework to construct highdimensional volatility connectedness network linking 65 major currencies. Empirical results indicate that the US dollar (USD) and Euro are major volatility transmitters while other currencies including Japanese yen and British pound are basically net volatility receivers. In volatility connectedness network, currencies tend to be clustered according to geographical distributions. Dynamically, total volatility connectedness reacts sensitively to changes in international economic fundamentals and increases during crisis periods. Directional volatility connectedness of Renminbi has decreased significantly since the reforms of the Chinese exchange rate regime (which shifts from a USD-pegged exchange rate regime to a regulated, managed floating exchange rate regime). Generally, oil exports, forex regimes and monetary policies are major factors driving volatility transmission across global forex markets.

Suggested Reviewers:

Xiangyun Gao [email protected] We suggest Prof. Gao to be a potential reviewer for our manuscript in that he has deep insight into the research on financial network, financial markets, and energy economics. He has published many related papers in such journals as International Review of Financial Analysis, Energy Economics, Journal of Economic Interaction and Coordination, Energy Policy, Emerging Markets Finance and Trade, Applied Energy, Renewable & Sustainable Energy Reviews, Energy, etc.

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Abstract:

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Wei-Xing Zhou [email protected] We suggest Prof. Zhou to be a potential reviewer for our manuscript in that he has deep insight into the research on financial network, financial markets, and risk management. He is an associate editor of Journal of Network Theory in Finance. Yachun Gao [email protected] We suggest Dr. Gao to be a potential reviewer for our manuscript in that he has deep insight into the research on financial network and risk management. For example, one of Dr. Gao’s works is referenced in our study, see, Gao, Y.C., Zeng, Y., Cai, S.M., 2015. Influence network in the Chinese stock market. Journal of Statistical Mechanics: Theory and Experiment 2015, P03017.

Response to Reviewers:

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Response to Reviewers (without Author Details)

Response to Reviewers

Manuscript number: MULFIN 2019 209 Title: Volatility Connectedness in Global Foreign Exchange Markets Journal: Journal of Multinational Financial Management 29 January 2020

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Dear Prof. P´eter Szil´agyi and Reviewers,

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We appreciate two reviewers’ insightful comments on our manuscript. The suggestions are helpful and we have incorporated them into our revised version. We are indebted to the reviewers for their time and consideration. We have taken all the points seriously, and have revised the manuscript accordingly. Below we provide our item-by-item response to each concern. The changes in the revised manuscript are marked by red font and in the LATEX file the command “\textcolor{red}{}” is employed. We hope our responses to the comments and our revisions for the original manuscript will meet with approval.

Yours sincerely,

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Anonymous authors.

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Kind regards.

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Reply to Comments of Reviewer #1 The paper is well-written, I really enjoyed reading it. After a long time, I actually don’t have any major comments, just two suggestions: 1. First of all, there are a lot of network studies, which are totally neglected (mostly published in Physica A, e.g. Vyrost et al., 2015; Baumohl et al., 2018, Kang and Lee, 2019, Zhang et al., 2019 and many others. Some network studied can be also found elsewhere, but their appearance is rather low, e.g. in Finance Research Letters). I would suggest to look at some of these works as well. Response:

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Thank you for your kind comments and insightful suggestions. We added following contents in Sec. 1.2 to supplement our literature review in the second part of the Introduction with plenty of network studies as follows: “The volatility spillover network has also been widely applied to other financial systems, e.g., commodity price indexes (Diebold et al., 2018), different financial markets in a specific country (Wang et al., 2016), global equity markets (Kang and Lee, 2019) and financial institutions (Wang et al., 2018). In addition to correlation-based networks and the volatility spillover network, financial networks based on other econometric approaches including the mean spillover network and the tail risk spillover network have also been extensively used to uncover information transmission mechanisms among financial agents. Billio et al. (2012) propose a Granger causalitybased mean spillover network for measuring systemic risk of financial institutions. The mean spillover network is also applied to global stock markets (V´yrost et al., 2015; Baum¨ohl et al., 2018) and Korean financial system (Song et al., 2016). The tail risk network is developed by Hautsch et al. (2015) to quantify the systemic importance of financial entities based on the least-absolute shrinkage and selection operator (LASSO) method. Other tail risk spillover networks include tail-event driven network (TENET) (H¨ardle et al., 2016) and extreme risk spillover network (Wang et al., 2017), which concentrate on systemic interconnectedness across financial institutions. More recently, spatial spillover networks are constructed to investigate multidimensional spillover effect across financial entities (Zhang et al., 2019).” (Please see the first footnote on Page 4 in the revised manuscript.)

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2. There are still few typos and grammatical errors (e.g. Cholesy-factor), one more careful reading is needed. Response:

Thank you for your suggestion. In the revised manuscript, we made multiple rounds of careful proofreading as you suggested. References ¨ & Baum¨ohl, E. (2015). Granger causality stock market networks: V´yrost, T., Ly´ocsa, S., Temporal proximity and preferential attachment. Physica A: Statistical Mechanics and its Applications, 427, 262-276. 2

¨ & V´yrost, T. (2018). Networks of volatility spilloverBaum¨ohl, E., Ko¨cenda, E., Ly´ocsa, S., s among stock markets. Physica A: Statistical Mechanics and its Applications, 490, 15551574. Kang, S. H., & Lee, J. W. (2019). The network connectedness of volatility spillovers across global futures markets. Physica A: Statistical Mechanics and its Applications, 526, 120756. Zhang, W., Zhuang, X., & Li, Y. (2019). Dynamic evolution process of financial impact path under the multidimensional spatial effect based on G20 financial network. Physica A: Statistical Mechanics and its Applications, 121876. Response:

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Thank you for this recommendation. The suggested references are cited in the revised manuscript.

References

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ˇ V´yrost, T., 2018. Networks of volatility spillovers Baum¨ohl, E., Koˇcenda, E., Ly´ocsa, S., among stock markets. Physica A: Statistical Mechanics and its Applications, 490, 1555–1574. Billio, M., Getmansky, M., Lo, A.W., Pelizzon, L., 2012. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104, 535 – 559. Diebold, F.X., Liu, L., Yılmaz, K., 2018. Commodity connectedness, in: Mendoza, E.G., Pastn, E., Saravia, D. (Eds.), Monetary Policy and Global Spillovers: Mechanisms, Effects, and Policy Measures. Bank of Chile Central Banking Series, Santiago. volume 25 of Monetary Policy and Global Spillovers: Mechanisms, Effects, and Policy Measures, pp. 97–136. H¨ardle, W.K., Wang, W., Yu, L., 2016. TENET: Tail-event driven NETwork risk. Journal of Econometrics, 192, 499–513. Hautsch, N., Schaumburg, J., Schienle, M., 2015. Financial network systemic risk contributions. Review of Finance 19, 685–738. Kang, S.H., Lee, J.W., 2019. The network connectedness of volatility spillovers across global futures markets. Physica A: Statistical Mechanics and its Applications, 526. Song, J.W., Ko, B., Cho, P., Chang, W., 2016. Time-varying causal network of the korean financial system based on firm-specific risk premiums. Physica A: Statistical Mechanics and its Applications, 458, 287 – 302. ˇ V´yrost, T., Stefan Ly´ocsa, Baum¨ohl, E., 2015. Granger causality stock market networks: Temporal proximity and preferential attachment. Physica A: Statistical Mechanics and its Applications, 427, 262 – 276. Wang, G.J., Xie, C., He, K., Stanley, H.E., 2017. Extreme risk spillover network: Application to financial institutions. Quantitative Finance, 17, 1417–1433. Wang, G.J., Xie, C., Jiang, Z.Q., Eugene Stanley, H., 2016. Who are the net senders

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and recipients of volatility spillovers in Chinas financial markets? Finance Research Letters, 18, 255–262. Wang, G.J., Xie, C., Zhao, L., Jiang, Z.Q., 2018. Volatility connectedness in the Chinese banking system: Do state-owned commercial banks contribute more? Journal of International Financial Markets, Institutions and Money, 57, 205–230. Zhang, W., Zhuang, X., Li, Y., 2019. Dynamic evolution process of financial impact path under the multidimensional spatial effect based on G20 financial network. Physica A: Statistical Mechanics and its Applications, 532, 121876.

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Reply to Comments of Reviewer #3

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This paper studies the volatility connectedness of 65 currencies in the foreign exchange market, uses the volatility spill over index to measure the interaction between currencies volatility, and combines the lasso-var model to solve the problem of parameter estimation of high-dimensional samples. It calculated the volatility spill over index of each currency, constructs networks to provide an overview of pairwise directional connectedness for 65 currencies. At the same time, it points out the important driving factors for transmitting foreign exchange market fluctuations. In conjunction with China’s Renminbi exchange rate system reform, it explains the exchange rate reform for the impact on China’s connection with the foreign exchange market, it has a certain practical guiding significance, and to some extent represents the current development direction. There are some innovations in research methods, but there are still the following problems:

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(1) For Table 1, it is recommended to add the exchange rate regime to which the currency belongs;

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Response:

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Thank you for your comments and valuable advice. In the revised manuscript, we added a column of “ExRegime” to Table 1, clarifying the exchange rate regime to which the currency belongs. The data are taken from the Annual Report on Exchange Arrangements and Exchange Restrictions 2018 published by the International Monetary Fund (IMF). Note that “Cb”, “Cp”, “Ns” and “St” are short for exchange rate arrangements defined as currency board, conventional peg, no separate legal tender and stabilized arrangement, respectively, according to the IMF. In addition, the currency maintains an exchange rate anchor to the US dollar, Euro or a currency composite when the symbol in the bracket is USD, EUR or Composite correspondingly. In details, we added the following text in Sec. 3: “For convenience of further investigations, the region and the exchange rate regime to which the currency belongs are also provided as the columns of “Region” and “ExRegime” in Table 1. The data of exchange rate regimes are taken from the Annual Report on Exchange Arrangements and Exchange Restrictions 2018 published by the International Monetary Fund (IMF).1 ” (Please see Lines 273–278 and the third footnote on Page 11 and Page 31 in the revised manuscript.)

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See the Annual Report on Exchange Arrangements and Exchange Restrictions 2018 published by the IMF (https://www.imf.org/˜/media/Files/Publications/AREAER/ areaer-2018-overview.ashx) on 16 April 2019.

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ExRegime Anchor Anchor Free Floating Free Floating Free Floating Free Floating Floating Crawl-like Free Floating Floating Free Floating St (Composite) Cb (USD) Free Floating Floatng Floatng Free Floating Floating Floating Floating Cp (EUR) Free Floating Free Floating Floating Floating Floating Cp (USD) Floating Floating Free Floating Stabilized Floating Floating

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Region North America Europe Asia Europe Oceania North America Europe Asia Europe Oceania Latin America Asia Asia Europe Asia Europe Europe Asia Latin America Africa Europe Europe Asia Asia Asia Europe Middle East Europe Middle East Latin America Asia Latin America Asia

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TV 4437.55 1590.57 1095.56 648.58 348.31 260.41 243.42 202.06 112.32 104.01 97.06 91.48 87.7 84.72 83.84 72.81 58.08 57.95 50.69 49.29 42.38 35.32 32.12 18.24 18.09 15.3 15.15 14.23 14 12.46 10.09 7.9 7.04

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Currency US Dollar Euro Japanese Yen British Pound Australian Dollar Canadian Dollar Swiss Franc Chinese Yuan Swedish Krona New Zealand Dollar Mexican Peso Singapore Dollar Hong Kong Dollar Norwegian Kroner North Korean Won New Turkish Lira Russian Rouble Indian Rupee Brazilian Real South African Rand Danish Krone Polish Zloty Taiwan Dollar Thai Baht Malaysian Ringgit Hungarian Forint Saudi Arabian Riyal Czech Koruna Israeli Shekel Chilean Peso Indonesian Rupiah Colombian Peso Philippine Peso

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Symbol USD EUR JPY GBP AUD CAD CHF CNY SEK NZD MXN SGD HKD NOK KRW TRY RUB INR BRL ZAR DKK PLN TWD THB MYR HUF SAR CZK ILS CLP IDR COP PHP

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Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

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Table 1: 65 currencies and their symbols, trading volumes (averaged TVs in billions of USD per day), rank of TVs (as of April, 2016), regions and exchange rate regimes. Notes: 65 currencies fall into seven regions: North America, Europe, Asia, Oceania, Latin America, Africa, and Middle East. The last twenty eight currencies together account for less than 1.1% of total trading volumes in global forex markets, whose detailed data are not reported by the BIS so that we use “—” to represent their TVs. ExRegime is short for exchange rate regime, and Cb, Cp, Ns and St are short for exchange rate arrangements defined as currency board, conventional peg, no separate legal tender and stabilized arrangement, respectively, according to the IMF. The currency maintains an exchange rate anchor to the US dollar, Euro or a currency composite when the symbol in the bracket is USD, EUR or Composite correspondingly. Rank 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Symbol RON PEN BGN BHD AED BDT BSD CUP DZD ECS EGP GNF GTQ HRK HTG ISK JMD KWD KYD KZT LAK LBP LKR MAD NGN OMR PAB QAR TND UGS VND XOF

Currency Romanian New Leo Peruvian Nuevo Sol Bulgarian Lev Bahraini Dinar United Arab Emirates Dirham Bangladesh Taka Bahamian Dollar Cuban Peso Algerian Dinar Ecuador Sucre Egyptian Pound Guinea Franc Guatemala Quetzal Croatian Kuna Haiti Gourde Iceland Krona Jamaican Dollar Kuwaiti Dinar Cayman Islands Dollar Kazakhstan Tenge Lao Kip Lebanese Pound Sri Lanka Rupee Moroccan Dirham Nigerian Naira Omani Rial Panama Balboa Qatar Rial Tunisian Dinar Ugandan Shilling Vietnamese Dong CFA Franc BCEAO

TV 4.82 3.88 1.26 0.37 — — — — — — — — — — — — — — — — — — — — — — — — — — — —

Region Europe Latin America Europe Middle East Middle East Asia Latin America Latin America Africa Latin America Africa Africa Latin America Europe Latin America Europe Latin America Middle East Latin America Asia Asia Middle East Asia Africa Africa Middle East Latin America Middle East Africa Africa Asia Africa

ExRegime Floating Floating Free Floating Cp (USD) Cp (USD) Crawl-like Cp (USD) Other Other Ns (USD) Stabilized Cp (EUR) Stabilized St (EUR) Crawl-like Floating Floating Cp (Composite) Other Floating Crawl-like St (USD) Crawl-like Cp (Composite) Stabilized Cp (USD) Ns (USD) Cp(USD) Crawl-like Floating St (Composite) Cp (EUR)

(2) “Global forex markets are highly interconnected compared with many other financial markets or assets”, This conclusion had better add TVC (total volatility connectedness) data for each market or asset, and briefly explain the reason; Response:

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Thank you for your valuable suggestion. We updated the following content in Sec. 4.1: “The total volatility connectedness (TVC) for 65 currencies reaches 71.79%, which is far higher than that for four different assets with a value of 12.6% (Diebold and Yılmaz, 2012), global equity markets with a value of 39.5% (Diebold and Yılmaz, 2009), commodity price indexes with a value of 40% (Diebold et al., 2018), and cryptocurrencies with a value of 37.79% (Yi et al., 2018), but is slightly lower than that for financial institutions in the United States with a value of 78.3% (Diebold and Yılmaz, 2014) and in China with a value of 85.53% (Wang et al., 2018). Therefore, global forex markets are highly interconnected compared with many other financial markets or assets. We should stress that due to increasing needs of external trade and investments, speculation as well as hedge, frequent transaction and huge trading volumes of forex assets endow forex markets with sufficient liquidity so that major traded currencies as included in our sample can scarcely be isolated from any volatility shocks of other currencies.” (Please see Lines 309–323 on Pages 12 in the revised manuscript.)

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(3) How to determine the high connectedness rankings of HKD, PAB is caused by the exchange rate mechanism factors, why not other factors? As the impact of the exchange rate regime on the volatility transmission is emphasized in the conclusion of this article, the reasons need to be explained in detail. The cited literature needs to be marked.

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Thank you for calling our attention to this concern. We hope that the following detailed explanation will eliminate your doubts: “According to Table 1, HKD and PAB are anchored to USD under currency board and no separate legal tender arrangements, respectively. The monetary policies of fixed exchange rates pegged directly give rise to extremely similar trends in exchange rates of HKD and PAB to that of USD, making them passive volatility receivers of USD that plays the role of a strong, free floating currency. In summary, their strong relationships with USD increase both from-degree and to-degree connectedness of HKD and PAB. Besides, the high to-degree connectedness of HKD may also partly stem from the significant financial influence exerted by Hong Kong as the global financial center and the offshore Renminbi center. Correspondingly, the high connectedness ranking of HKD can be explained jointly by its large trading volume, exchange rate regime and the important financial position of Hong Kong in the world, while that of PAB may largely stem from the indirect effect of USD due to its fixed exchange rate anchored to USD.” (Please see Lines 363–376 on Pages 13 and 14 in the revised manuscript.) (4) How to determine the high connectedness rankings of AED, BHD, SAR, OMR is caused by the oil export factors, why not other factors? please explain.

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Thank you for pointing out this concern. At first, we hold that both oil exports and exchange rate mechanisms play significant roles in the high connectedness ranking of these currencies (i.e., AED, BHD, SAR and OMR), as mentioned in Section 4.1.2 According to Table 1, all these currencies are pegged to USD, and their high connectedness rankings might be attributed to the high connectedness ranking of USD as well. We strived to support our view with relevant investigations and added the following contents in Section 4.1: “An extensive body of literature focusing on the dependence structure between oil and currencies provides available evidence for the relationship between oil exports and forex markets (see, e.g., Alam et al., 2019; Gao et al., 2014; Li et al., 2017; Mensi et al., 2017; Singh et al., 2018). Mensi et al. (2017) argue that some currencies act as net volatility transmitters to oil market, while others receive net volatility shocks from oil market, which indicates that oil exports possibly serve as a medium of volatility transmission across currencies. Besides, it is also found that exchange rates of oil-importing countries and oil-exporting countries are influenced asymmetrically by oil markets (Yang et al., 2017). Furthermore, how these two factors, oil exports and exchange rate arrangements, work with each other in volatility transmission between Middle Eastern currencies and others is further discussed on the basis of network visualization in Section 4.2.3 ” (Please see Lines 383–395 and the fourth footnote on Page 14 in the revised manuscript.)

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(5) The article mentioned that the US dollar has a significant volatility spill over effect on the euro. Is it possible that the dominant role of the euro in other currencies due to indirect effect of the US dollar? How to ensure that the “US dollar and Euro are major volatility transmitters” conclusion?

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Thank you for calling our attention to this concern. To answer your questions, we may turn to the definition of volatility spillover index as given by Eq. (3), which measures the proportion of currency i’s forecast error variance (i.e., volatility) that can be explained by currency j. On this basis, we make the inference that Euro is a major volatility transmitter according to the fact that it accounts for substantial proportion of volatility in many other currencies. While the significant volatility spillover from USD to Euro indicates that the former largely determines how great volatility of the latter is, it does not necessarily exert any influence on volatility transmission between Euro and other currencies. Given that Euro adopts a free floating exchange rate which are completely independent of USD, we can hardly jump to the conclusion that the dominant role of Euro in other currencies is due to USD. We can only say that the influence of Euro on other currencies may be partly due to the “indirect effect” of USD. As a proof, the net volatility spillovers from Euro and USD to some currencies are given 2

Please see Lines 380–383 on Page 14 in the revised manuscript. In addition, other factors including bilateral trade volume, foreign investment and distance, may play a part in volatility spillover across currencies according to the empirical analysis on the major determinants of forex markets by Peng et al. (2019). 3

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USD 2.22 1.71 1.40 0.86 0.72 0.26 0.74 0.88 0.66 0.71 1.25 0.35 1.06 0.63 1.22 0.87 1.08

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EUR 3.62 4.24 2.15 1.41 1.28 0.28 1.16 1.36 0.92 1.31 1.51 0.50 1.88 0.91 1.25 1.62 1.44

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From MAD TND JPY CZK HUF ISK NOK PLN RUB SEK CHF TRY DKK BRL CLP AUD NZD

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Table R1: Net volatility spillovers from Euro and USD to other currencies in percentage points.

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in Table R1. It can be noticed that Euro contributes greater volatility spillovers to these currencies even than USD, suggesting that the influence of Euro on these currencies is greater than that of USD on them. Hence the conclusion that USD and Euro are major volatility transmitters can be ensured through empirical results obtained. Anyway, your questions are of great interest and deserve to be discussed in our further investigations.

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(6) What is the difference between out/in-degree and page-rank when assessing whether a currency is a volatility transmitter or receiver? Please explain Why the natural resources in rich Middle Eastern countries are lower in out- degree but higher in page Rank? Response:

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Thank you for calling our attention to this concern. At first, it should be pointed out that out/in-degree rather than PageRank serves as the criteria to assess whether a currency is a volatility transmitter or receiver. To make our explanation more clear, we added the following contents in Section 4.2: “Out-degree and in-degree of a node are generally defined as the number of edges converging at and emerging from it, respectively. Note that directions of edges in volatility connectedness networks as shown in Fig. 3 correspond to volatility spillover directions between currencies. Then a node with a higher out-degree but a lower in-degree tends to contribute more volatility shocks than it receives, whereas a node with a higher in-degree but a lower out-degree receives more volatility shocks than it contributes in the financial system. Therefore, the former plays the role of a volatility transmitter while the latter are considered as a volatility receiver. In contrast, the PageRank centrality measures the importance of nodes from a different perspective based on the network topology structure. As a variant of eigenvalue centrality, the PageRank centrality is originally adopted in web search engine and then is applied to directed graphs in the field of network science. Specifically, the PageRank of node i is determined 9

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recursively by the PageRanks of its neighbor nodes (Brin and Page, 1998) and is defined ∑ eik A eik is the volatility as PRi = α N PRk + β, where α and β are constants,4 A k=1,k̸=i sout k connectedness from k to i ranging from 0 and 1 as defined by Eq. (13) and sout is the k ∑N e 5 out out-strength of node k (sk = j=1 Ajk ). It is clear by definition that the PageRank centrality of a node depends on the number of links it receives as well as the centrality and link propensity of the linkers. To summarize, a node is important in terms of the PageRank centrality if it attracts more links or if it is linked from other important nodes. Unlike the out-degree and in-degree, the PageRank centrality of a node rests with properties of links it receives rather than its own property.” (Please see Lines 424–448 on Pages 15 and 16 as well as the fifth footnote on Page 15 and the sixth footnote on Page 16 in the revised manuscript.)

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According to Table 5, we find that the currencies of several natural-resource-rich Middle Eastern countries with lower out-degree (e.g., KWD and QAR) tend to be higher in indegree, and therefore they receive more links from other currencies. Hence they have a higher PageRank centrality according to the definition mentioned above.

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References

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In addition, we modified the following contents in Section 4.2: “Given that TRY, RUB, ILS, COP and ZAR receive significant volatility shocks from many other currencies according to their relatively high in-degrees, it is unsurprising that they are the top 5 currencies ranked by the PageRank centrality.” (Please see Lines 513–517 on Page 18 in the revised manuscript.)

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Alam, M.S., Shahzad, S.J.H., Ferrer, R., 2019. Causal flows between oil and forex markets using high-frequency data: Asymmetries from good and bad volatility. Energy Economics, 84, 104513. Brin, S., Page, L., 1998. The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems, 30, 107–117. Diebold, F.X., Liu, L., Yılmaz, K., 2018. Commodity connectedness, in: Mendoza, E.G., Pastn, E., Saravia, D. (Eds.), Monetary Policy and Global Spillovers: Mechanisms, Effects, and Policy Measures. Bank of Chile Central Banking Series, Santiago. volume 25 of Monetary Policy and Global Spillovers: Mechanisms, Effects, and Policy Measures, pp. 97–136. Diebold, F.X., Yılmaz, K., 2009. Measuring financial asset return and volatility spillovers, with application to global equity markets. The Economic Journal, 119, 158–171. Diebold, F.X., Yılmaz, K., 2012. Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting, 28, 57–66. 4

As in Brin and Page (1998), here the value of α is set 0.85 and that of β is set at 0. Note that when computing the PageRank centrality of each node, we also consider the case of the (0, 1) e (i.e., A eik is one or zero and sout is the out-degree of node k), finding that the results adjacency matrix of A k are similar. 5

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Diebold, F.X., Yılmaz, K., 2014. On the network topology of variance decompositions: Measuring the connectedness of financial firms. Journal of Econometrics, 182, 119– 134. Gao, X., An, H., Fang, W., Li, H., Sun, X., 2014. The transmission of fluctuant patterns of the forex burden based on international crude oil prices. Energy, 73, 380 – 386. Li, X.P., Zhou, C.Y., Wu, C.F., 2017. Jump spillover between oil prices and exchange rates. Physica A: Statistical Mechanics and its Applications, 486, 656 – 667. Mensi, W., Hammoudeh, S., Shahzad, S.J.H., Al-Yahyaee, K.H., Shahbaz, M., 2017. Oil and foreign exchange market tail dependence and risk spillovers for MENA, emerging and developed countries: VMD decomposition based copulas. Energy Economics, 67, 476–495. Peng, W., Hu, S., Chen, W., Zeng, Y.f., Yang, L., 2019. Modeling the joint dynamic value at risk of the volatility index, oil price, and exchange rate. International Review of Economics & Finance 59, 137–149. Singh, V.K., Nishant, S., Kumar, P., 2018. Dynamic and directional network connectedness of crude oil and currencies: Evidence from implied volatility. Energy Economics, 76, 48–63. Wang, G.J., Xie, C., Zhao, L., Jiang, Z.Q., 2018. Volatility connectedness in the Chinese banking system: Do state-owned commercial banks contribute more? Journal of International Financial Markets, Institutions and Money, 57, 205–230. Yang, L., Cai, X.J., Hamori, S., 2017. Does the crude oil price influence the exchange rates of oil-importing and oil-exporting countries differently? A wavelet coherence analysis. International Review of Economics & Finance, 49, 536 – 547. Yi, S., Xu, Z., Wang, G.J., 2018. Volatility connectedness in the cryptocurrency market: Is Bitcoin a dominant cryptocurrency? International Review of Financial Analysis, 60, 98–114.

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Highlights

Highlights: • High-dimensional volatility connectedness networks for 65 forex markets are constructed using the LASSO-VAR approach. • Global forex markets are highly interconnected compared with many other financial markets or assets.

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• Oil exports and forex regimes increase systemic importance of weak currencies in terms of volatility transmission.

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• USD and Euro are major volatility transmitters while most currencies including JPY and GBP are net volatility receivers.

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• Renminbi’s volatility connectedness decreases significantly after China’s exchange rate reforms.

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Title Page

Volatility Connectedness in Global Foreign Exchange Markets Tiange Wena , Gang-Jin Wanga,b,∗ a

Business School, Hunan University, Changsha 410082, China Center for Finance and Investment Management, Hunan University, Changsha 410082, China

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Abstract

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We statically and dynamically measure total and directional volatility connectedness in global foreign exchange (forex) markets. We use the volatility spillover index and LASSOVAR approaches in the variance decomposition framework to construct high-dimensional volatility connectedness network linking 65 major currencies. Empirical results indicate that the US dollar (USD) and Euro are major volatility transmitters while other currencies including Japanese yen and British pound are basically net volatility receivers. In volatility connectedness network, currencies tend to be clustered according to geographical distributions. Dynamically, total volatility connectedness reacts sensitively to changes in international economic fundamentals and increases during crisis periods. Directional volatility connectedness of Renminbi has decreased significantly since the reforms of the Chinese exchange rate regime (which shifts from a USD-pegged exchange rate regime to a regulated, managed floating exchange rate regime). Generally, oil exports, forex regimes and monetary policies are major factors driving volatility transmission across global forex markets.

Key words: forex markets, volatility connectedness, volatility spillover, financial

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network, currency JEL: F31, G15, C32

Acknowledgements

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This work was supported by the National Natural Science Foundation of China (Grant nos. 71871088, 71501066, 71850006, 71971079, and 71521061), the Huxiang Youth Talent Support Program and the Hunan Provincial Natural Science Foundation of China (Grant no. 2017JJ3024).



Corresponding author at: Business School of Hunan University, 11 Lushan South Road, Yuelu District, Changsha 410082, China. Email addresses: [email protected] (Tiange Wen), [email protected] (Gang-Jin Wang) Preprint submitted to Journal of Multinational Financial Management January 28, 2020

Manuscript

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Volatility Connectedness in Global Foreign Exchange Markets

Abstract

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We statically and dynamically measure total and directional volatility connectedness in global foreign exchange (forex) markets. We use the volatility spillover index and LASSO-VAR approaches in the variance decomposition framework to construct high-dimensional volatility connectedness network linking 65 major currencies. Empirical results indicate that the US dollar (USD) and Euro are major volatility transmitters while other currencies including Japanese yen and British pound are basically net volatility receivers. In volatility connectedness network, currencies tend to be clustered according to geographical distributions. Dynamically, total volatility connectedness reacts sensitively to changes in international economic fundamentals and increases during crisis periods. Directional volatility connectedness of Renminbi has decreased significantly since the reforms of the Chinese exchange rate regime (which shifts from a USD-pegged exchange rate regime to a regulated, managed floating exchange rate regime). Generally, oil exports, forex regimes and monetary policies are major factors driving volatility transmission across global forex markets.

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1. Introduction

1.1. Background Since the 2008 global financial crisis, much attention has been paid to the connectedness among finanical entities due to the “too connectedned to fail” problem. To quantitatively measure the volatility connectedness among financial markets and which ones influence each other, Diebold and Yılmaz (2009, 2012) propose the volatility spillover index approach based on variance decompositions of vector auto-regression (VAR) models. The volatility

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Key words: forex markets, volatility connectedness, volatility spillover, financial network, currency JEL: F31, G15, C32

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Preprint submitted to Journal of Multinational Financial Management January 29, 2020

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1.2. Motivation and Literature The first strand of literature on volatility connectedness across global forex markets mainly studies about volatility transmission among major traded currency pairs (see, e.g., Barun´ık et al., 2017; Kenourgios et al., 2015a,b; Greenwood-Nimmo et al., 2016; Kilic, 2017; Salisu and Ayinde, 2018; Salisu et al., 2018), volatility spillover from a strong currency (e.g., Euro) to other weak currencies in specific regions as the most discussed Asia (e.g., Ito, 2017; Sehgal et al., 2017; Shu et al., 2015), Europe (e.g., Bub´ak et al.,

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spillover index approach provides a useful tool for portfolio managers and policy makers in diversifying risk, assessing market stability or formulating regulatory policy. It is also extended to the high-dimensional volatility spillover network (Diebold and Yılmaz, 2014; Demirer et al., 2018; Yi et al., 2018) for uncovering the systematically important financial markets and volatility transmission mechanism in the global financial system. Forex markets attract widespread interests among investors for decentralization and a relatively lower entry barrier. The huge trading volumes and continuous operations on trading days make them sensitive to changes in the political and financial environment. Macro news release and government intervention are generally believed to exert significant influence on volatility in forex markets. To be more specific, forex markets react differently according to timing and approaches of macro news release as well as origins and types of announcement matters (Ben Omrane et al., 2017; Li et al., 2015; Vajda et al., 2015; Koˇcenda and Moravcov´a, 2018). As for the effect of government intervention, central bank transparency and quantitative easing announcements take a great part (Catal´an-Herrera, 2016; Kenourgios et al., 2015b; Weber, 2019; Viola et al., 2019). Besides, volatility in currency markets is also influenced by trade nexus and investor behavior (Coudert et al., 2015; Goddard et al., 2015). Under the background, we investigate both total and directional volatility connectedness in global forex markets with the introduction of network theory and explore possible economic and policy factors on volatility connectedness. Our results show that volatility connectedness networks exhibit characteristics that relate directly to local political and economic situation, and total volatility connectedness reacts sensitively to both economic and political shocks especially during volatile periods. Besides, we also figure out the contributions of different currencies in volatility connectedness across global forex markets. Our research provides adequate references for both monetary policy makers and market participants.

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2011; Antonakakis, 2012; Orlowski, 2016; Koˇcenda and Moravcov´a, 2019), and countries along “the belt and the road” (e.g., Li et al., 2018; Mai et al., 2018) or dependence structure between currencies with other markets including stock markets (e.g., Boako and Alagidede, 2017; Kumar et al., 2019), crude oil (e.g., Mensi et al., 2017; Singh et al., 2018), other commodities (e.g., Boubakri et al., 2019; Khalifa et al., 2016) and cryptocurrencies (e.g., Baum¨ohl, 2019). Prior works tend to lay more emphasis on the effect of policy factors (e.g., QE announcements, exchange rate regimes, central bank interventions under inflation or exchange rate targeting, capital controls, and forex reserves) and economic factors (e.g., financial crisis, trade linkage, oil exports, investor behavior and trade deficits) on volatility transmission across currencies. Nevertheless, most of them focus on a small number of major currencies in forex markets, and ignore that much uncertainty still exists about roles of weak currencies in the forex market network. Another strand of literature links to the network topology structure of forex markets based on correlation-based networks. Correlation-based networks, e.g., the minimum spanning tree (MST) (Mantegna, 1999) and the planar maximally filtered graph (PMFG) (Tumminello et al., 2005), are generally used to examine relations between different currencies, and node properties in networks are discussed to illustrate the impact of individual currency. Previous studies using correlation-based networks (see, e.g., Baydilli and T¨ urker, 2019; Cao et al., 2017; Karmakar, 2017; Kumar et al., 2019; Li et al., 2018; Mai et al., 2018; Mensi et al., 2017; Singh et al., 2018; Wang et al., 2016) show that (i) nodes with higher degrees, e.g., USD and CNY, tend to play more significant roles in the forex market network, (ii) there is a small-world effect in the forex market network, and (iii) geographical clusters are typically observed in high dimensional forex market network, which can be explained by international trade, political and cultural relationships. However, most of the correlation-based networks, which are built on linear correlations between returns of market data and are undirected networks, cannot reflect volatility connectedness or spillovers across forex markets and the lead-lag relationship between forex markets. To fill the gap in the previous literature, our work here constructs a high-dimensional volatility connectedness network linking 65 major currencies for examining connectedness in global forex markets based on the volatility spillover index and the LASSO-VAR approach. The volatility spillover index of Diebold and Yılmaz (2009) derives from the Cholesky-factor variance decomposition proposed by Sims (1980). Diebold and Yılmaz (2012) further

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develop the volatility spillover index to make the results robust to variable orderings using the KPPS generalized variance decomposition method (Koop et al., 1996; Pesaran and Shin, 1998). With directed and weighted networks in the variance decomposition framework, Diebold and Yılmaz (2014) propose the volatility spillover network and provide a glimpse of how to extract more information through network topology. By extension, Diebold et al. (2018) observe strong clustering effects within several traditional industry groupings and further estimate network connectedness for group aggregation. Network visualization is an effective and instinctive way to present pairwise directional volatility connectedness for large samples. In these cases, however, heavy parameterization in traditional VAR model estimation restricts its applicability. To this end, Demirer et al. (2018) use the LASSO method for selecting and shrinking variables when estimating high-dimensional VARs, and apply it to constructing volatility connectedness network linking 96 banks in the world. Yi et al. (2018) build a high-dimensional volatility spillover network connecting 52 cryptocurrencies using the extension of LASSO-VAR, i.e., the VARX-L framework of Nicholson et al. (2017). The effectiveness of LASSO-VAR in dealing with high-dimensional data motivates us to use it in our work for constructing volatility connectedness network of forex markets.1 1

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The volatility connectedness (or spillover) network has also been widely applied to other financial systems, e.g., commodity price indexes (Diebold et al., 2018), different financial markets in a specific country (Wang et al., 2016), global equity markets (Kang and Lee, 2019) and financial institutions (Wang et al., 2018). In addition to correlation-based networks and the volatility spillover network, financial networks based on other econometric approaches including the mean spillover network and the tail risk spillover network have also been extensively used to uncover information transmission mechanisms among financial agents. Billio et al. (2012) propose a Granger causality-based mean spillover network for measuring systemic risk of financial institutions. The mean spillover network is also applied to global stock markets (V´ yrost et al., 2015; Baum¨ohl et al., 2018) and Korean financial system (Song et al., 2016). The tail risk network is developed by Hautsch et al. (2015) to quantify the systemic importance of financial entities based on the least-absolute shrinkage and selection operator (LASSO) method. Other tail risk spillover networks include tail-event driven network (TENET) (H¨ardle et al., 2016) and extreme risk spillover network (Wang et al., 2017), which concentrate on systemic interconnectedness across financial institutions. More recently, spatial spillover networks are constructed to investigate multidimensional spillover effect across financial entities (Zhang et al., 2019).

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1.4. Organizations The remaining part of the paper proceeds as follows. In Section 2, we introduce the volatility spillover index under the generalized variance decomposition framework, the LASSO-VAR method and network connectedness measures. In Section 3, we describe data sets and some preliminary statics of volatility series of currencies. In Section 4, we calculate and analyze the static and dynamic volatility connectedness among 65 currencies in forex markets. In Section 5, we conclude the paper.

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1.3. Main contributions Our study has the following contributions. First, it is the first attempt to investigate volatility connectedness among 65 currencies using the volatility spillover index approach of Diebold and Yılmaz (2014). Our work adds to both the literature on volatility connectedness or spillover and the literature on volatility transmission across forex markets through introducing the LASSO-VAR model and network theory. Much of previous research using Diebold and Yilmaz’s (2009; 2012) spllover index approach is confined to a narrow range of currencies which are geographically linked or most traded in the world, while other studies are limited to using undirected correlationbased networks linking a large number of currencies (see, e.g., Section 1.2). We fill the gap through constructing high-dimensional directed volatility spillover networks based on LASSO-VAR models and variance decompositions to figure out roles of both strong and weak currencies in volatility transmissions across global forex markets. Second, our empirical studies based on regional connectedness shed new light on potential volatility transmission channels other than market transactions, which are unnoticed by the existing research. Our results highlight oil exports, forex rate regimes and trade linkages among neighbor countries, which play an important part in volatility connectedness network for 65 major currencies in global forex markets. Finally, we investigate effects of economic and even political enviroment (e.g., Britain exiting from European Union in Section 4.4) as well as monetary policies on total and directional volatility connectedness and identify the periods when the strength of volatility connectedness shows a significant rising trend, which always coincide with dramatic changes in macro environment such as financial crisis. Besides, our results are robust to parameters (including the order lag p, predictive horizon H and rolling window width w) in LASSO-VAR models and volatility estimators V .

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2. Methodology 2.1. Volatility spillover index The volatility spillover index used in our work is based on a stationary p-th order N -variable VAR(p), which can be expressed as Yt = C +

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where Yt is a set of exchange rate volatility time series under consideration, C denotes an N -dimension constant intercept vector, Φi is an N ×N parameter matrix, and εt ∼ (0, Σ). Eq. (1) can be transformed into the moving average representation as ∞ X Yt = W + Ai εt−i (2) i=0

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where Ai is an N × N coefficient matrix that obeys the recursion Ai = Pp j=1 Φj At−j , and especially A0 is an N × N identity matrix. We follow Diebold and Yılmaz (2012) and use the generalized VAR variance decomposition method that is independent of variable orderings. The key issue in the spillover index approach is to figure out the proportion of currency i’s forecast error variance at horizon H that can be explained by currency j, i.e., H−1 X −1 σjj (e0i Ah Σej )2

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g θij (H) =

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h=0 H−1 X (e0i Ah ΣA0h ei ) h=0

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where σjj is the standard deviation of the error term in the j-th equation, ei denotes a selection vector with the i-th element being ones and others being zeros, and Σ is the variance matrix of error vector ε. The generalized VAR framework allows and accounts for correlated shocks, instead of striving to orthogonalize shocks, whichPmeans the total sums of variance shares are not g necessarily equal to 1, i.e., N j=1 θij (H) 6= 1. We thus normalize the directional connectedness from currency j to currency i as g θij (H) g θeij (H) = PN g (4) θ (H) j=1 ij

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P eg PN PN eg so that N j=1 θij (H) = 1 and i=1 j=1 θij (H) = N . On the above basis, we introduce three total directional connectedness of currency i: (i) from-degree connectedness, defined as total directional connectedness from all other currencies to currency i, i.e, PN

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and (iii) net-degree connectedness, defined as the difference between the todegree connectedness and the from-degree connectedness of currency i, i.e, g g (H) − Ci←· (H) Cig (H) = Ci→·

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Regional or sectoral clustering effects have been widely observed in previous studies (Baydilli and T¨ urker, 2019; Demirer et al., 2018; Diebold et al., 2018; Li et al., 2018; Mai et al., 2018; Wang et al., 2016, 2017). In this paper, the 65 considered forex markets are from seven regions: Africa, Asia, Europe, Latin America, Middle East, North America and Oceania. Following the sector level connectivity measure proposed in Wang et al. (2017), we introduce a measure of regional connectedness (RC) from one region m to another region n (itself included), which is defined as

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If Cig (H) > 0, currency i is a net transmitter of volatility connectedness, otherwise it is a net receiver of volatility connectedness. Furthermore, we introduce a system-wide connectedness measure, total volatility connectedness (TVC), defined as

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(6)

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(ii) to-degree connectedness, defined as total directional connectedness from currency i to all other currencies, i.e, g Ci→· (H)

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2.2. LASSO-VAR The parameter space of VAR models grows quadratically with the number of considered variables, rapidly using up the available degrees of freedom. In our study, the number of variables (forex markets), N , is equal to 65, and if we suppose the lag of VAR, p to be 3, then the number of regression parameters needed to be estimated is N 2 p+p, that is 11,910. This will lead to the inability of VARs for high-dimensional samples, while VARs have been empirically proved to be more accurate when allowing for more variables. It is also a major reason why most previous studies (see, e.g., Alley, 2018; Antonakakis, 2012; Barun´ık et al., 2017; Bub´ak et al., 2011; Kenourgios et al., 2015a; Li et al., 2018; Salisu et al., 2018; Sehgal et al., 2017) on volatility connectedness among currencies are restricted to a small number of sample. To clear the barrier, we follow Demirer et al. (2018) and Yi et al. (2018) and use the extension of LASSO-VAR framework proposed by Nicholson et al. (2017) to estimate volatility connectedness among 65 forex markets due to its effectiveness in reducing the parameter space of VAR and VARX models. Moreover, we apply the Lag Sparse Group LASSO penalty (Simon et al., 2013) that is fitted by the accelerated generalized gradient descent algorithms and can sparse the model space to the convex least square objective function

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where both m and n ∈ {Africa, Asia, Europe, Latin America, Middle East, North America, and Oceania}, Nm and Nn are the number of forex markets contained in region m and region n, respectively. Especially when m = n, Nn = Nm − 1 and i 6= j. In Eq. (9) we normalize connectedness between two regions by their forex market amounts for eliminating the sample size bias, because each region has a different number of forex markets in our sample.

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min u,Φ

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2.3. Network connectedness A network can be defined by an N × N adjacency matrix A composed of elements (or edges) Aij , i.e., A = {Aij }, in which Aij = 1 if node i and node j are connected, otherwise Aij = 0 if they are unconnected. In an undirected network, A is a symmetric matrix in which all the properties of the network are contained. What interests us is that the connectedness measures mentioned in Section 2.1 is associated with the concept of network connectedness. More specifically, the variance decomposition or volatility g connectedness matrix, θeij (H) can be considered as the adjacency matrix of an weighted and directed network (also known as a volatility connectedness network), i.e., g Aij = θeij (H)

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N X j=1

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Total directional connectedness measures introduced in Section 2.1 correspond to network connnectedness statistics including degrees, degree distributions and distances. It can be inferred from Eqs. (5), (6), and (12) that the from-degree connectedness and to-degree connectedness equal to off-diagonal row and column sums, respectively. That is, the total directional connectg g edness measures Ci←· (H) and Ci→· (H) are exactly the from-degree and todegree of node i in the weighted directed network, respectively. Besides, the total volatility connectedness measure in Eq. (8) is precisely the mean degree of the network with diagonal entries excluded. It is evident by definition that the variance decomposition network is fully connected. However, a fully connected network tends to have too much

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g θeij (H) −

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Networks determined by variance decomposition matrix are, however, more sophisticated than traditional networks in three ways: (i) the entries are weights between zero and one rather than simply 0-1 with some potentially weak and others potentially strong, (ii) the adjacency matrix is not symmetric any more, in other words, the strength of the j → i link is not necessarily equal to that of the i → j link, which means the links between nodes are directed, and (iii) each row of the adjacency matrix must add to 1, which can be inferred from the Eq. (4). In addition, diagonal entries equal to one minus the from-degree connectedness instead of zero, that is,

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Accordingly, there arises the key question about the selection of appropriate threshold. To this end, we introduce the global efficiency (GE) (Latora and Marchiori, 2001) and network density (ND) measures of networks firstly, which respectively quantify efficiency of information exchange and intensity of connections over the network. Then we examine the evolution of GE and ND of the network under various connectedness thresholds and choose a specific threshold for filtering the fully connected network. The global efficiency and network density are defined respectively as

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noise embedded in it, which spurs us to filter the fully connected network into a spare network using a connectedness threshold for keeping the most significant volatility connectedness. Given a connectedness threshold θ, the e = {A eij } of a filtered volatility connectedelement in the adjacency matrix A ness network is defined as  eij = Aij if Aij ≥ θ A (13) 0 else

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ND =

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3. Data description and preliminary analysis Our data are forex rates of 65 major currencies from 29 November 2000 to 15 February 2019, taken from Datastream and Pacific Exchange Rate Service website (http://fx.sauder.ubc.ca/data.html). Following Wang et al. (2016), we choose the special drawing right (SDR) as the numeraire, which consists of a basket of currencies and embodies the whole changes in the world economy. Our samples include 37 of top 38 currencies ranked by their averaged trading volumes per day, which source from statistics from Bank for International

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where d(i, j) denotes the shortest path length from node i to j, d(i, j) = +∞ eji ) satisfies if there is no path from i to j in the network, and Ei→j = sign(A eji > 0, otherwise Ei→j = 0. that Ei→j = 1 if A

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Settlements (BIS) as of April 2016.2 The remaining 28 currencies together account for no more than 1.1% of total turnovers in global forex markets, and we use “—” to represent their trading volumes (TVs). Table 1 presents the 65 currencies’ symbols, TVs (averaged trading volumes in billions of USD) and rankings of TVs as of April 2016. For convenience of further investigations, the region and the exchange rate regime to which the currency belongs are also provided as the columns of “Region” and “ExRegime” in Table 1. The data of exchange rate regimes are taken from the Annual Report on Exchange Arrangements and Exchange Restrictions 2018 published by the International Monetary Fund (IMF).3 Following Antonakakis and Kizys (2015) and Wang et al. (2016), we use absolute value of daily continuously compound returns of currency i as its daily volatility estimator, that is, Vi,tabs = | ln Pi,t − ln Pi,t−1 |, where Pi,t and Pi,t−1 are exchange rates of currency i on day t and day t − 1 respectively. Each volatility series contains 4521 observations during the whole sample period. Figure 1 shows daily volatility series of the top 12 currencies with the largest averaged trading volumes per day. Among them, USD, EUR, CNY, and SGD are less volatile. The volatility trends of all currencies rose sharply during the 2008–2009 global financial crisis and the period from the second half of 2015 to the first half of 2016. Table 2 provides descriptive statistics of the 12 most traded currencies’ daily volatility series over the sample period. Volatility of USD is the lowest with an average value of 0.22%, followed by CNY, SGD and EUR. Standard deviations of USD and CNY are around 0.2%, smaller than that of other sample currencies, suggesting comparatively smooth moves in both currencies. By contrast, MXN and NZD are the most volatile ones, followed by AUD. Note that in Fig. 1, the volatile periods of NZD coincide with those of AUD, namely, both currencies almost share the same volatility curve. Full sample analysis in Section 4.3 will show that this phenomenon is not merely out of coincidence but driven by volatility transmission mechanisms of currency markets. In general, minor currencies are more susceptible to changes in global economic fundamentals and thus more unstable. Besides, the skew-

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See the foreign exchange turnover statistics provided by BIS (https://www.bis.org/ publ/rpfx16.htm). The data were last updated on 11 December 2016. 3 See the Annual Report on Exchange Arrangements and Exchange Restrictions 2018 published by the IMF (https://www.imf.org/~/media/Files/Publications/AREAER/ areaer-2018-overview.ashx) on 16 April 2019.

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ness and kurtosis values suggest a non-Gaussian distribution for all volatility series. All ADF statistics are far less than the test critical values at the 1% significant level, indicating that volatility series are stationary and suitable for further VAR modeling.

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4.1. Full-sample analysis In this section, static volatility connectedness table for 65 currencies over the entire period is estimated with LASSO-VAR models at the lag order p = 3 days and the forecast horizon H = 12 days. The total volatility connectedness (TVC) for 65 currencies reaches 71.79%, which is far higher than that for four different assets with a value of 12.6% (Diebold and Yılmaz, 2012), global equity markets with a value of 39.5% (Diebold and Yılmaz, 2009), commodity price indexes with a value of 40% (Diebold et al., 2018), and cryptocurrencies with a value of 37.79% (Yi et al., 2018), but is slightly lower than that for financial institutions in the United States with a value of 78.3% (Diebold and Yılmaz, 2014) and in China with a value of 85.53% (Wang et al., 2018). Therefore, global forex markets are highly interconnected compared with many other financial markets or assets. We should stress that due to increasing needs of external trade and investments, speculation as well as hedge, frequent transaction and huge trading volumes of forex assets endow forex markets with sufficient liquidity so that major traded currencies as included in our sample can scarcely be isolated from any volatility shocks of other currencies. Table 3 reports the top 10 directional connectedness (or edges) between pairwise currencies. The largest one is the volatility spillover from AUD to NZD (14.29%) and the opposite is exactly the second largest (12.85%). This can adequately explain why their volatility curves show such similar trends. Another interesting finding is that the third to the tenth largest volatility connectedness all have occurred among nine European currencies. Seven of them are none euro zone currencies of European Union (EU), while NOK and CHF are none EU currencies. We can by far draw the conclusion that the great influence of EU as a monetary and political bloc increases volatility transmission across European forex markets substantially. In particular, the pairwise directional connectedness between two emerging Central European (CE) currencies, i.e., PLN and HUF, rank the third (9.79%) and the fourth (9.13%), respectively. Another tightly connected

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pairwise CE currencies are CZK and DKK. Specifically, volatility connectedness from DKK to CZK is the sixth largest with 9.01% and that from CZK to DKK is the tenth largest with 8.06%. These results are similar to those reported by Bub´ak et al. (2011), who conduct an investigation on volatility transmission across the three CE currencies and EUR/USD. There also exists significant volatility connectedness between two Northern European (NE) currencies, i.e., NOK and SEK. The pairwise directional connectedness from SEK to NOK is the fifth largest with 9.05%, and in return, that from NOK to SEK is the seventh largest with 8.51%. As another NE currency, DKK is strongly connected with CHF. To further figure out which currencies play dominant roles in volatility transmission in global forex markets, in Table 4 we present the top 10 currencies ranked by from-degree connectedness, to-degree connectedness and net-degree connectedness respectively. We may notice at a first glance that the to-degree connectedness and net-degree connectedness rankings are almost identical. As the difference between to-degree connectedness and fromdegree connectedness, net-degree connectedness is mainly dependent on the former because from-degree connectedness varies within a comparatively narrow range from 0 to 1. USD, PAB and HKD are always the top three currencies ranked by any of from-degree, to-degree and net-degree connectedness. Although large trading volumes may contribute to the significant influence of USD (ranking 1st) and HKD (ranking 13th), the exchange rate mechanism is a potential reason for HKD and PAB with high connectedness rankings because they are pegged to USD, meaning that (i) USD is the really dominant currency in forex markets and (ii) some of the influence of HKD and PAB may be attributed to the influence of USD. According to Table 1, HKD and PAB are anchored to USD under currency board and no separate legal tender arrangements, respectively. The monetary policies of fixed exchange rates pegged directly give rise to extremely similar trends in exchange rates of HKD and PAB to that of USD, making them passive volatility receivers of USD that plays the role of a strong, free floating currency. In summary, their strong relationships with USD increase both from-degree and to-degree connectedness of HKD and PAB. Besides, the high to-degree connectedness of HKD may also partly stem from the significant financial influence exerted by Hong Kong as the global financial center and the offshore Renminbi center. Correspondingly, the high connectedness ranking of HKD can be explained jointly by its large trading volume, exchange rate regime and the important financial position

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4.2. Network visualization of static volatility connectedness We construct threshold networks (i.e., filtered volatility connectedness networks) to provide an overview of pairwise directional connectedness for 65 currencies. As in Schweitzer et al. (2009) and Gao et al. (2015), we first determine the connectedness threshold by examining the changes of global efficiency and network density as the connectedness threshold adjusts. In Fig. 2 we plot the variation of network properties including network density and global efficiency under various connectedness threshold levels. Network density decreases significantly as the connectedness threshold level increases,

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of Hong Kong in the world, while that of PAB may largely stem from the indirect effect of USD due to its fixed exchange rate anchored to USD. The next highest-ranked currencies are four Middle East currencies (AED, BHD, SAR and OMR) and one Latin America currency (BSD), among which AED, BSD and SAR swap their positions in from-degree connectedness rankings compared with to-degree and net-degree connectedness rankings. Oil exports (of the four Middle East countries) and exchange rate regimes pegged to USD (of all the five countries) are two possible determinant factors for their high rankings. An extensive body of literature focusing on the dependence structure between oil and currencies provides available evidence for the relationship between oil exports and forex markets (see, e.g., Alam et al., 2019; Gao et al., 2014; Li et al., 2017; Mensi et al., 2017; Singh et al., 2018). Mensi et al. (2017) argue that some currencies act as net volatility transmitters to oil market, while others receive net volatility shocks from oil market, which indicates that oil exports possibly serve as a medium of volatility transmission across currencies. Besides, it is also found that exchange rates of oil-importing countries and oil-exporting countries are influenced asymmetrically by oil markets (Yang et al., 2017). How these two factors (i.e., oil exports and exchange rate arrangements) work with each other in volatility transmission between Middle Eastern currencies and others is further discussed on the basis of the network visualization in Section 4.2.4 On the whole, Table 4 shows that a few minor currencies contribute significantly to volatility connectedness, highlighting other channels of volatility transmission than forex market transactions.

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In addition, other factors including bilateral trade volume, foreign investment and distance, may play a part in volatility spillover across currencies according to the empirical analysis on the major determinants of forex markets by Peng et al. (2019).

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while movements of global efficiency are relatively moderate. Finally we set the connectedness threshold at 0.01 to obtain more instinctive information with little loss of efficiency at the same time. Figure 3 presents a snapshot of volatility connectedness network for 65 currencies during the entire sample period when the connectedness threshold θ = 0.01. The network is characterized by the properties of both nodes and edges as follows. Firstly, the nodes are classified and colored according to regions of currencies (see Table 1), and their sizes are determined by out-degree and in-degree of currencies respectively in Fig. 3(a) and 3(b). Secondly, directions of edges indicate directions of the corresponding volatility spillover between currencies. Especially, the color of a directed edge is the same as that of the ending node and the starting node respectively in Fig. 3(a) and 3(b). At last, the width of edges indicates the strength of volatility connectedness, meaning that the thicker an edge, the stronger the corresponding volatility connectedness. In Table 5, we list three node centralities including out-degree, in-degree and PageRank to measure the importance of currencies in the network. Outdegree and in-degree of a node are generally defined as the number of edges converging at and emerging from it, respectively. Note that directions of edges in volatility connectedness networks as shown in Fig. 3 correspond to volatility spillover directions between currencies. Then a node with a higher out-degree but a lower in-degree tends to contribute more volatility shocks than it receives, whereas a node with a higher in-degree but a lower out-degree receives more volatility shocks than it contributes in the financial system. Therefore, the former plays the role of a volatility transmitter while the latter are considered as a volatility receiver. In contrast, the PageRank centrality measures the importance of nodes from a different perspective based on the network topology structure. As a variant of eigenvalue centrality, the PageRank centrality is originally adopted in web search engine and then is applied to directed graphs in the field of network science. Specifically, the PageRank of node i is determined recursively by the PageRanks of its neighbor nodes (Brin and Page, 1998) and is defined P eik A eik is PRk + β, where α and β are constants,5 A as PRi = α N k=1,k6=i sout k the volatility connectedness from k to i ranging from 0 and 1 as defined by

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As in Brin and Page (1998), here the value of α is set at 0.85 and that of β is set at 0.

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PN e 6 Eq. (13) and sout is the out-strength of node k (sout = It is k k j=1 Ajk ). clear by definition that the PageRank centrality of a node depends on the number of links it receives as well as the centrality and link propensity of the linkers. To summarize, a node is important in terms of the PageRank centrality if it attracts more links or if it is linked from other important nodes. Unlike the out-degree and in-degree, the PageRank centrality of a node rests with properties of links it receives rather than its own property. To facilitate analysis, currencies are ranked by out-degree in descending order. Note that in Table 5, nodes with a high out-degree, which are almost the same as currencies with the high to-degree connectedness in Table 4, tend to be of a low in-degree. Although similar to the concept of directional connectedness (from-degree and to-degree connectedness), degree centralities (i.e., out-degree and in-degree) highlight the role (volatility transmitter or receiver) of each node in any given pairwise directional connectedness, further revealing volatility transmission mechanisms of global forex markets. In what follows, we develop the discussion based on the analysis of both Fig. 3 and Table 5. To begin with, USD’s node size is the greatest in Fig. 3(a) with an outdegree of 42 and the smallest in Fig. 3(b) with a zero in-degree. Namely Fig. 3 shows that USD transmits volatility shocks to many other currencies in a widespread and substantial way, while it almost receives no shock from any other currencies. Reviewing Fig. 1, we can reach a conclusion that USD is relatively stable itself and hardly susceptible to shocks from other currencies, and its volatility during crisis periods spills over to a wide range of currencies exponentially. As far as we are concerned, USD can be considered as a welldeserved dominant currency in global forex markets in terms of volatility transmission. According to Fig. 3(a), there are significant volatility spillover from USD to a bunch of Middle East, Asian and Latin American currencies, who depend heavily on USD in the matter of exchange rate mechanisms or oil settlements. Similarly, EUR shows similar dominance in volatility connectedness network with an out-degree of 34 and an in-degree of 12, when taking no account of minor currencies pegged to USD or EUR (from PAB to XOF in Table 5). Besides, volatility spillover from USD to EUR is significant.

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Note that when computing the PageRank centrality of each node, we also consider the e (i.e., A eik is one or zero and sout is the out-degree case of the (0, 1) adjacency matrix of A k of node k), finding that the results are similar.

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What is interesting to note is that Middle East currencies fall into three categories by the similar behavior: the first contains AED, SAR, OMR and BHD, which also play significant roles in Table 4, the second includes KWD, QAR and ILS, and the last is LBP. In the first category, the four currencies are of great sizes in Fig. 3(a) (with large out-degrees), but have significantly small sizes in Fig. 3(b) (with small in-degrees), while the opposite behavior holds in the second category. As an exception, however, the size of LBP keeps the same in both subgraphs. This can also be directly observed by the comparison of out-degree and in-degree in Table 5. To find the reason, we notice that all the above Middle East countries except for Israeli are exporters of oil and gasoline in the world, and adopt an exchange rate mechanism fixed on USD. The balance between volatility transmission through resource exports and volatility reception via exchange rate mechanisms and trading settlements of these countries is the main reason for the difference. That is to say, volatility transmission effect weights over volatility reception effect for the five currencies in the first category, while the opposite happens in the second category. As a validation, United Arab Emirates and Saudi Arab are top 5 oil exporters in the world, while Qatar ranks behind ten other countries and Israeli is not an oil exporter. Moreover, Fig. 3 exhibits that Middle East currencies are highly interconnected within the region. Currencies from Oceania and several non-euro zone currencies of EU are highly interconnected respectively as observed earlier in Table 3. To summarize, currencies tend to cluster according to geographical distributions. Both Fig. 3(a) and Table 5 show that most of minor currencies in Asia, Africa and Europe are mainly volatility receivers during the entire sample period and only transmit weak volatility shocks to other currencies in the same region. Generally, the difference between node’s size in Fig. 3(a) and that in Fig. 3(b) or more intuitively, the difference between node’s out-degree and in-degree in Table 5, indicates net volatility connectedness of the corresponding currency. For example, all the top 10 currencies ranked by net-degree connectedness (i.e., net volatility transmitters) in Table 4 show a remarkably high out-degree in both Fig. 3(a) and Table 5 and a low in-degree in both Fig. 3(b) and Table 5. PageRank centrality in Table 5 provides auxiliary information for identifying systemically important nodes in volatility connectedness network. Note that SGD (0.0165), MYR (0.0179) and CAD (0.0195) have a higher PageRank centrality compared to other currencies, and their out-degrees outnumber more than half of the 65 currencies at the same time. Hence, these nodes play

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4.3. Regional connectedness Currencies in Fig. 3 show a strong tendency to cluster within regions such as Middle East, Oceania, as well as northern and central Europe. Following Wang et al. (2017), we propose a measure of regional connectedness as Eq. (9) to investigate the widely observed group aggregation (a regional clustering effect in our case) in financial networks. Table 6 provides estimations of regional connectedness, where from-degree and to-degree connectedness equal to off-diagonal row and column sums respectively, and net-degree connectedness is the difference between to-degree and from-degree. Within-region connectedness (diagonal elements) are notably greater than cross-region connectedness (off-diagonal elements) with exceptions for Africa and America. It is proved once again in Table 6 that two currencies (i.e., AUD and NZD) in Oceania are highly interconnected by the largest regional connectedness with 13.57%. Following that, there are Middle East and Europe. Moreover, North America and Middle East are the two largest regions ranked by both from-degree and to-degree connectedness, indicating the strong influence of USD and oil exports. Asia and Latin America are the third and fourth largest from-degree and to-degree respectively, which are both emerging financial markets in the world. At last, the seven regions fall into two groups by signals of net-degree connectedness: the first group contains Africa, Asia, Europe and Oceania, which are all volatility receivers with negative netdegree connectedness; and the second group includes Latin America, Middle East and North America, which are volatility transmitters with positive netdegree connectedness. To obtain more intuitive results, we characterize cross-region network connectedness in Fig. 4, where node’s size is determined by to-degree, edge’s

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important roles in volatility transmission in terms of information flow. Given that TRY, RUB, ILS, COP and ZAR receive significant volatility shocks from many other currencies according to their relatively high in-degrees, it is unsurprising that they are the top 5 currencies ranked by the PageRank centrality. It should be noticed that all the local countries of these currencies except for ILS, i.e., Turkey, Russia, Columbia and South Africa, take a dominant role in exports of strategic natural resources including oil, gas, coal and minerals. Such a phenomenon indicates that commodity exports increase the importance of these currencies in volatility transmission, which may serve as the medium of volatility transmission instead of making direct contribution to volatility shocks or connectedness through commodity exports.

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4.4. Rolling sample analysis To capture secular and cyclical movements in volatility spillover, we estimate volatility connectedness using 120-days windows (i.e., w = 120). Besides, VAR lag p is set at 3 days, and forecast horizon H is set at 12 days. We start with the examination of time-varying evolution of system-wide connectedness, i.e., total volatility connectedness (TVC) as plotted in Fig. 5. One may notice at once that the TVC fluctuates at high levels (from 65% to 90%) during the whole sample period, confirming the preliminary conclusion that global forex markets are highly interconnected generally. Specifically, the TVC went through three major cycles as results of some relevant events. The first cycle started in November 2000 with 71.70%, and ended in January 2007 with 70.45%. The first maximum value of TVC arrived at 78.37% in June 2001, and it stood at the highest point over the circle at 84.10% in April 2002, then subsided sharply. In the second half of 2000, American stock markets suffered from dot com bubble bust, and the oil price increased as well as the Euro depreciation sent Europe into recession. These information came as bad news for forex markets, increasing both volatility and volatility transmission of USD and Euro. World economy began to recover in the second half of 2001, increasing the volatility connectedness among currencies. Another interesting part of the plot is that volatility connectedness increased from 72.51% in July 2003 to 81.17% in April 2004. The result may be explained by the USD depreciation and the good performance of global stock markets in the second half of 2003. The second cycle lasted from January 2007 with 70.45% to February 2014 with 71.49%, when forex markets went through a volatile period as well. One may naturally think of the 2008 global financial crisis and the subsequent

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color follows its starting nodes, and edge’s width corresponds to strength of the regional connectedness. Both North America and Middle East transmit a considerable amount of volatility to all other regions, playing dominant roles in regional connectedness. As emerging economies, Latin America and Asia are the second tier, either receiving or transmitting volatility from or to other parts of the world. Africa and Oceania are net volatility receivers, transmitting no volatility to any other regions. For the former, its financial markets are under a primitive state of development, hardly in any volatility connectedness with global financial markets. For the latter, forex markets in Oceania show a significant regional clustering effect, while exerting almost no influence on other regions.

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European debt crisis. To begin with, TVC was pushed up to a small peak at 82.68% in August 2007 by the credit crunch. Then it climbed to the highest point at 87.31% in May 2008, mere months after the stock and forex markets panic as well as Bear Stearns’ takeover by JP Morgan in March 2008. After decreasing slightly, TVC was taken to the extreme again at 82.88% in November 2008 by collapse of the Lehman Brothers, then subsided until June 2009. After hitting the bottom in June 2009, TVC showed an upward trend with Greek debt crisis looming in the second half of 2009 and then reached 85.31% in January 2010. From December 2010 to September 2012, TVC fluctuated between 75% and 85%. It was not until February 2014 that TVC reached a record low at 71.49%. The third cycle started in February 2014 with 71.49% and ended in July 2017 with 67.61%, which concerns the referendum vote on Brexit (i.e., Britain exiting from European Union). The variation in this period is relatively smooth compared with the first two circles. TVC rose to a maximum value at 83.42% in June 2015. Note that then prime minister Cameron decided to bring precede the vote. This unexpected information increased uncertainty about the future of British pound and Euro, leading to the increase of both volatility and volatility connectedness in forex markets. However, when the vote was held in June 2016, the TVC plot only showed a slight upward trend. A possible explanation for this might be that the vote result is in line with the expectation of investors. Following the three circles, system-wide volatility connectedness remained low despite small fluctuations since the second half of 2017. In Figs. 6–8 we present dynamic from-degree, to-degree and net-degree connectedness of the top and bottom sixteen currencies ranked by average strengths of corresponding directional connectedness over the entire period, respectively. Currencies are listed in descending order by strengths of directional volatility connectedness. What stands out in Fig. 6 is that colors of top 16 currencies are dominated by red during the sample period. Except that USD and Euro take leading roles in forex trading and volatility transmission across global forex markets (see Table 4), others are minor currencies and adopt fixed exchange rates pegged to USD or EUR. Exchange rate mechanisms explain why over 80% of volatility in these minor currencies are attributed to major currencies (USD or Euro). Lower trading volumes and less control of local monetary authorities make the currencies passive receivers of volatility shocks. By contrast, the from-degree connectedness of the bottom 16 currencies in Fig. 6 varies widely across rolling-sample

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windows. These currencies are relatively stable and hardly susceptible to volatility shocks from other currencies for being traded more frequently and their independent forex regimes. Their from-degree connectedness keeps low during calm periods while rises sharply during volatile periods identified in Fig. 5. Compared with the from-degree connectedness in Fig. 6, the to-degree connectedness in Fig. 7 varies widely across currencies. The top 16 currencies range in colors from green to orange (i.e., the to-degree connectedness ranges from 120% to 180%), while the bottom 16 currencies are in colors dominated with dark blue (i.e., the to-degree connectedness is under 40%). Among the top 16 currencies, USD and its pegged currencies are the first tier; and EUR and XOF (that is pegged to EUR) are the second tier. Hong Kong has relatively mature financial markets and Middle East has a strong voice in oil exports. Correspondingly, their currencies exert influence on other currencies by themselves except for contribution of USD. Similar to that in Fig. 6, the bottom 16 currencies in Fig. 7 include lots of important currencies such as AUD, CAD, JPY and GBP. They are in colors dominated by blue with their to-degree connectedness below 40% for most of the time. This finding actually denies the existence of a positive relationship between trading volumes and volatility transmission of currencies except for USD and EUR. What is striking about Fig. 7 is that to-degree connectedness of CNY decreases significantly since the beginning of 2006. By the end of sample period, the color of CYN reduced to blue. China’s exchange rate reforms have contributed to the decline in the to-degree connectedness of CNY. In June 2005, the monetary policy of CNY transferred from a fixed exchange rate pegged to USD to a managed floating exchange rate pegged to a basket of currencies for the first time. After that, Chinese monetary authorities widened the trading band of CNY/USD in May 2007, resulting in a short period when the to-degree connectedness kept low until 2008. During the global financial crisis from July 2008 to June 2010, the monetary policy of CNY moved back to a fixed exchange rate pegged to USD as an emergency measure against financial risks. Hence, its to-degree connectedness rose to a high level as USD, though this phenomenon disappeared after the fixed forex regime of CNY was abolished in June 2010. The net-degree connectedness is the difference between the to-degree connectedness and the from-degree connectedness, and its variation shown in Fig. 8 resembles that of the to-degree connectedness, because the from-degree connectedness varies within a narrow range from zero to one. The 16th cur-

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4.5. Robustness analysis Here we check the robustness of our empirical results to several key parameters of the models. In details, we examine the sensitivity of total volatility connectedness for the VAR lag p, the forecast horizon H, the rolling window width w, and the volatility estimator V in Figs. 9–11. For convenience, one or two parameters are compared in each figure with other parameters unchanged. Table 7 provides a guide on values of the four parameters in each one of Figs. 9–11. In Fig. 9, we consider forecast horizons H at 9 and 15 days as well as window widths w at 90 and 150 days as a supplement to the forecast horizon H = 12 days and window width w = 120 days. It is apparent from Fig. 9 that choices of forecast horizons and window widths show little influence on our results. Similarly, the six TVC curves corresponding to VAR lags from 1 to 6 in Fig. 10 show virtually the same trend, indicating that our results are robust to the choice of VAR lags as well. To investigate the robustness of our results to volatility estimators V , we take another two estimation methods including V sqrt and V GARCH into account, which are respectively defined by:

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rency ranked by average net-degree connectedness, EUR, is in a color ranging from blue to shallow green for most of the time, with its net-degree connectedness slightly above zero. Therefore, only few currencies (from USD to EUR shown in Fig. 8) are net volatility transmitters, while most currencies are net volatility receivers. Even among the bottom 16 currencies appear several actively traded currencies such as CAD, JPY and GBP. Generally, USD has the greatest value in terms of dynamic from-degree, to-degree and net-degree connectedness according to Figs. 6–8, which confirms again that USD is the dominant currency in volatility connectedness across global forex markets. This finding is consistent with that of Wang et al. (2016) who focus on tail dependence structure of 42 currencies in the world. Following that it is EUR, when taking no account of minor currencies that are pegged to USD or EUR.

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Vi,tsqrt = (ln Pi,t − ln Pi,t−1 )2

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ri,t = βi ri,t−1 + ui,t , ui,t ∼ t(f ) GARCH 2 (Vi,tGARCH )2 = αi,0 + αi,1 (Vi,t−1 ) + αi,2 u2i,t−1

(17)

where ri,t denotes return of currency i on day t, α and β are estimated coefficients, and ui,t denotes residual error. Three TVC curves based on three volatility estimators in Fig. 11 share similar qualitative features, suggesting 22

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In this paper, we examine total and directional volatility connectedness both statically and dynamically among 65 currencies in global forex markets from 29 November 2000 to 15 February 2019. Our work is based on VAR models and variance decomposition, and the empirical results are robust to related parameters in the models. In contrast to previous literature focusing on volatility spillover among a few currencies, we further introduce the LASSO to estimate VARs in high-dimensional circumstances and construct volatility connectedness network across global forex markets. In general, we find that currencies are highly interconnected compared with other assets, and their total volatility connectedness is only next to that of financial institutions. The most obvious finding is that US dollar acts as the well-deserved dominant currency in terms of volatility connectedness. Besides, oil exports and forex regimes play a significant role in volatility transmission across forex markets as well. A prominent feature of volatility connectedness network is that currencies tend to cluster according to geographical distributions. A prime example is two Oceania currencies (i.e., Australian dollar and New Zealand dollar). Forex markets in Central and Northern Europe are highly connected, while volatility connectedness between Euro and non-euro zone currencies is not significant. Another interesting conclusion is that the level of volatility connectedness or spillover of a currency does not necessarily depends on its trading volume. Two most important currencies, US dollar and Euro, are major volatility transmitters, while most other currencies including even Japanese yen and British pound are net volatility receivers. Based on regional connectedness measures, we find that within-region connectedness are significantly higher than cross-region connectedness. Moreover, we find that North America and Middle East propagate large volatility shocks to other regions, while Africa and Oceania tend to receive volatility shocks from others. Total volatility connectedness among 65 currencies shows periodical fluctuation during the sample period and increases sharply amid market uncertainty. Particularly,

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that our results are far from being sensitive to the choice of volatility estimators. In summary, there only exists slight differences among curves for varying window forecast horizons, window widths, VAR lags and volatility estimators, implying that our results are robust to choices of key parameters in VAR models.

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total volatility connectedness has remained at lower levels since July 2017, suggesting that global forex markets are much less volatile and fit for risk diversification in recent years. Dynamic directional volatility connectedness of Chinese Yuan indicates that the exchange rate reform by the Chinese authority plays an important role. To summarize, the mechanism of volatility transmission among 65 currencies is mainly dependent on three possible factors including oil exports, forex regimes and monetary policies besides market transactions. The regional clustering effect suggests that tight trade linkages and unity of policy among neighboring countries increase volatility connectedness among the currencies. Besides, the total volatility connectedness across global forex markets is highly susceptible to international economic fundamentals. Our investigations of volatility connectedness across global forex markets and examination of roles that each currency plays add to the literature on currencies and provide valuable information for both investors and policy makers. Firstly, our work contributes to the study of volatility connectedness among global forex markets. Our empirical results support evidence that US dollar is the leading currency in forex markets and there are significant clustering effects in volatility connectedness network. Taking 65 currencies into account, we provide comprehensive information regarding the volatility transmission mechanism of global forex markets. Secondly, the total volatility connectedness can serve as an indicator of market uncertainty and market stress to a certain extent. To illustrate the point, the plot of system-wide volatility connectedness shows a significant upward trend when forex markets are shocked by exogenous events or experiencing volatile periods. Hence, it will signal to market participants in time for market instability or potential losses in portfolios under unfavorable conditions when used appropriately. Finally, our study sheds new light on the relationships among currencies and depicts volatility connectedness among 65 currencies both statically and dynamically. Portfolio managers and investors will find the results useful when they devote to risk diversification or hedge against specific currencies. It is also instructive for policy makers in identifying volatile markets and making decisions regarding domestic currency.

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Ben Omrane, W., Tao, Y., Welch, R., 2017. Scheduled macro-news effects on a Euro/US dollar limit order book around the 2008 financial crisis. Research in International Business and Finance 42, 9–30. Billio, M., Getmansky, M., Lo, A.W., Pelizzon, L., 2012. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics 104, 535 – 559.

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Alley, I., 2018. Oil price and USD-Naira exchange rate crash: Can economic diversification save the Naira? Energy Policy 118, 245–256.

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Jo

TV 4437.55 1590.57 1095.56 648.58 348.31 260.41 243.42 202.06 112.32 104.01 97.06 91.48 87.7 84.72 83.84 72.81 58.08 57.95 50.69 49.29 42.38 35.32 32.12 18.24 18.09 15.3 15.15 14.23 14 12.46 10.09 7.9 7.04

lP

Currency US Dollar Euro Japanese Yen British Pound Australian Dollar Canadian Dollar Swiss Franc Chinese Yuan Swedish Krona New Zealand Dollar Mexican Peso Singapore Dollar Hong Kong Dollar Norwegian Kroner North Korean Won New Turkish Lira Russian Rouble Indian Rupee Brazilian Real South African Rand Danish Krone Polish Zloty Taiwan Dollar Thai Baht Malaysian Ringgit Hungarian Forint Saudi Arabian Riyal Czech Koruna Israeli Shekel Chilean Peso Indonesian Rupiah Colombian Peso Philippine Peso

na

Symbol USD EUR JPY GBP AUD CAD CHF CNY SEK NZD MXN SGD HKD NOK KRW TRY RUB INR BRL ZAR DKK PLN TWD THB MYR HUF SAR CZK ILS CLP IDR COP PHP

ur

31

Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

re

-p

Table 1: 65 currencies and their symbols, trading volumes (averaged TVs in billions of USD per day), rank of TVs (as of April, 2016), regions and exchange rate regimes. Notes: 65 currencies fall into seven regions: North America, Europe, Asia, Oceania, Latin America, Africa, and Middle East. The last twenty eight currencies together account for less than 1.1% of total trading volumes in global forex markets, whose detailed data are not reported by the BIS so that we use “—” to represent their TVs. ExRegime is short for exchange rate regime, and Cb, Cp, Ns and St are short for exchange rate arrangements defined as currency board, conventional peg, no separate legal tender and stabilized arrangement, respectively, according to the IMF. The currency maintains an exchange rate anchor to the US dollar, Euro or a currency composite when the symbol in the bracket is USD, EUR or Composite correspondingly. Region North America Europe Asia Europe Oceania North America Europe Asia Europe Oceania Latin America Asia Asia Europe Asia Europe Europe Asia Latin America Africa Europe Europe Asia Asia Asia Europe Middle East Europe Middle East Latin America Asia Latin America Asia

ExRegime Anchor Anchor Free Floating Free Floating Free Floating Free Floating Floating Crawl-like Free Floating Floating Free Floating St (Composite) Cb (USD) Free Floating Floatng Floatng Free Floating Floating Floating Floating Cp (EUR) Free Floating Free Floating Floating Floating Floating Cp (USD) Floating Floating Free Floating Stabilized Floating Floating

Rank 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Symbol RON PEN BGN BHD AED BDT BSD CUP DZD ECS EGP GNF GTQ HRK HTG ISK JMD KWD KYD KZT LAK LBP LKR MAD NGN OMR PAB QAR TND UGS VND XOF

Currency Romanian New Leo Peruvian Nuevo Sol Bulgarian Lev Bahraini Dinar United Arab Emirates Dirham

Bangladesh Taka Bahamian Dollar Cuban Peso Algerian Dinar Ecuador Sucre Egyptian Pound Guinea Franc Guatemala Quetzal Croatian Kuna Haiti Gourde Iceland Krona Jamaican Dollar Kuwaiti Dinar Cayman Islands Dollar Kazakhstan Tenge Lao Kip Lebanese Pound Sri Lanka Rupee Moroccan Dirham Nigerian Naira Omani Rial Panama Balboa Qatar Rial Tunisian Dinar Ugandan Shilling Vietnamese Dong CFA Franc BCEAO

TV 4.82 3.88 1.26 0.37 — — — — — — — — — — — — — — — — — — — — — — — — — — — —

Region Europe Latin America Europe Middle East Middle East Asia Latin America Latin America Africa Latin America Africa Africa Latin America Europe Latin America Europe Latin America Middle East Latin America Asia Asia Middle East Asia Africa Africa Middle East Latin America Middle East Africa Africa Asia Africa

ExRegime Floating Floating Free Floating Cp (USD) Cp (USD) Crawl-like Cp (USD) Other Other Ns (USD) Stabilized Cp (EUR) Stabilized St (EUR) Crawl-like Floating Floating Cp (Composite) Other Floating Crawl-like St (USD) Crawl-like Cp (Composite) Stabilized Cp (USD) Ns (USD) Cp(USD) Crawl-like Floating St (Composite) Cp (EUR)

Table 2: Descriptive statistics for daily volatility series of top 12 currencies ranked by averaged trading volumes per day during the sample period from 30 November 2000 to 15 February 2019. Notes: ADF is the augmented Dickey-Fuller test for testing the sample stability, whose null hypothesis is that the time series contains a unit root. We enlarge the mean, median, maximum and minimum values of all volatility series by 100 times for convenience of expression. Max.

Min.

Std. Dev.

Skewness

Kurtosis

ADF

0.2164 0.2576 0.3985 0.3079 0.4746 0.4077 0.3834 0.2239 0.4721 0.5214 0.5557 0.2305

0.1659 0.1938 0.2936 0.2255 0.3429 0.3067 0.2846 0.1724 0.3534 0.3841 0.4066 0.1783

2.630 2.140 5.062 6.959 8.293 3.048 17.769 2.539 4.763 6.609 8.594 2.600

0.0068 0.0001 0.0002 0.0000 0.0000 0.0002 0.0001 0.0001 0.0001 0.0000 0.0004 0.0000

0.0020 0.0024 0.0039 0.0032 0.0053 0.0037 0.0046 0.0020 0.0045 0.0052 0.0056 0.0021

2.061 1.956 2.907 4.371 4.858 1.951 14.432 2.089 2.421 2.963 3.449 2.434

12.597 9.260 20.694 56.011 50.166 8.858 482.650 12.395 13.771 20.463 28.655 15.171

−35.660 −34.050 −34.335 −33.729 −35.076 −31.926 −39.522 −34.752 −32.405 −35.450 −32.816 −32.237

lP ur na Jo 32

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of

Median

re

USD EUR JPY GBP AUD CAD CHF CNY SEK NZD MXN SGD

Mean

To i

g θeij (H)

1 2 3 4 5 6 7 8 9 10

AUD NZD PLN HUF SEK DKK NOK DKK DKK CZK

NZD AUD HUF PLN NOK CZK SEK SEK CHF DKK

0.1429 0.1285 0.0979 0.0913 0.0905 0.0901 0.0851 0.0845 0.0845 0.0806

ro

From j

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Rank

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Table 3: Top 10 directional connectedness (or edges) from currency j to currency i ranked g (H) (see Eq. (4)) during the sample period from 30 November 2000 to 15 by values of θeij g February 2019. Notes: θeij (H) denotes the strength of directional volatility connectedness or spillover from currency j to currency i.

ur na

Table 4: Top 10 currencies ranked by from-degree connectedness (left panel), to-degree connectedness (middle panel), and net-degree connectedness (right panel) during the sample period from 30 November 2000 to 15 February 2019. Notes: “Cur.” and “RTV” are short for currency and rank of trading volumes respectively. Rank

To-degree connectedness

Net-degree connectedness

Cur.

g Ci←· (H)

RTV

Cur.

g Ci→· (H)

RTV

Cur.

Cig (H)

RTV

USD PAB HKD AED BSD SAR OMR BHD KYD CNY

0.9435 0.9432 0.9427 0.9411 0.9410 0.9410 0.9373 0.9359 0.9314 0.9293

1 61 13 39 41 27 60 38 53 8

USD PAB HKD BSD SAR AED OMR BHD XOF EUR

1.8488 1.8384 1.8323 1.8109 1.7580 1.7567 1.6541 1.6077 1.5373 1.5370

1 61 13 41 27 39 60 38 66 2

USD PAB HKD BSD SAR AED OMR BHD XOF EUR

0.9053 0.8951 0.8896 0.8699 0.8170 0.8157 0.7168 0.6718 0.6124 0.6122

1 61 13 41 27 39 60 38 66 2

Jo

1 2 3 4 5 6 7 8 9 10

From-degree connectedness

33

Table 5: Node centralities (including out-degree, in-degree and PageRank) of 65 currencies in volatility connectedness network. Out-degree

In-degree

PageRank

Currency

Out-degree

In-degree

PageRank

USD PAB HKD AED BSD SAR XOF EUR OMR BHD KYD CNY ECS LBP VND HRK CZK PLN GTQ HUF DKK MAD SEK AUD SGD NOK KWD QAR MXN LKR MYR CAD TWD

42 41 39 38 37 36 35 34 33 31 28 27 27 21 18 18 17 17 15 14 14 13 13 13 12 12 11 11 9 8 8 8 7

0 1 2 3 4 5 11 12 6 7 8 9 10 13 14 17 5 6 15 6 4 20 8 10 23 8 18 16 8 19 21 11 22

0.0059 0.0062 0.0064 0.0066 0.0069 0.0072 0.0087 0.0095 0.0075 0.0079 0.0082 0.0085 0.0091 0.0100 0.0105 0.0123 0.0089 0.0095 0.0114 0.0109 0.0082 0.0153 0.0121 0.0112 0.0165 0.0143 0.0137 0.0118 0.0115 0.0145 0.0179 0.0195 0.0193

ZAR JPY PEN KRW BRL NZD BDT RON IDR PHP GBP THB KZT CLP COP ILS BGN EGP NGN DZD TND UGS GNF INR LAK ISK RUB CHF TRY CUP HTG JMD

6 6 6 5 5 5 4 3 3 3 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

14 12 20 10 13 9 21 21 18 19 15 22 17 7 8 12 17 5 12 9 9 18 6 19 20 5 4 9 11 1 12 23

0.0305 0.0137 0.0178 0.0253 0.0304 0.0166 0.0173 0.0120 0.0139 0.0183 0.0188 0.0251 0.0099 0.0242 0.0429 0.0477 0.0164 0.0062 0.0073 0.0066 0.0093 0.0100 0.0063 0.0170 0.0151 0.0193 0.0528 0.0115 0.0644 0.0061 0.0074 0.0220

ro

-p

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lP

ur na

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Currency

Table 6: Regional connectedness table. Note: table elements are normalized as in Eq. (9) to eliminate the sample size bias due to different amounts of currencies in different regions.

Jo

Africa Asia Europe Latin America Middle East North America Oceania To-degree Net-degree

Africa

Asia

Europe

Latin America

Middle East

North America

Oceania

From-degree

0.62 0.65 0.72 0.63 0.76 0.67 0.61 4.03 −2.37

0.77 1.21 0.65 0.98 1.26 1.14 0.91 5.70 −1.97

0.76 0.60 1.86 0.61 0.58 0.99 1.16 4.70 −1.05

1.09 1.36 0.83 1.49 1.84 1.55 0.76 7.44 0.34

1.8 2.27 1.14 2.24 3.30 2.28 0.83 10.54 3.24

1.54 1.99 1.37 2.07 2.57 0.62 1.78 11.32 3.20

0.44 0.81 1.05 0.59 0.28 1.49 13.57 4.65 −1.39

6.40 7.67 5.75 7.11 7.30 8.13 6.04 / /

34

of ro -p

re

Table 7: A guide on values of the four parameters in each one of Figs. 9–11. Forecast horizon H

VAR lag p

Volatility estimator V

90, 120, 150 120 120

9, 12, 15 12 12

3 1, 2, . . . , 6 3

V abs V abs abs sqrt V ,V , V GARCH

Jo

ur na

Fig. 9 Fig. 10 Fig. 11

lP

Window width w

35

EUR

JPY

0.05

0 2001 2004 2007 2010 2013 2016 2019

0.05

0 2001 2004 2007 2010 2013 2016 2019

GBP

0 2001 2004 2007 2010 2013 2016 2019

AUD

0.05

CAD

0.05

0 2001 2004 2007 2010 2013 2016 2019

0.05

0 2001 2004 2007 2010 2013 2016 2019

CNY

0.05

SEK

0.05

0 2001 2004 2007 2010 2013 2016 2019

0.05

0 2001 2004 2007 2010 2013 2016 2019

NZD

MXN

SGD

0.05

0 2001 2004 2007 2010 2013 2016 2019

0.05

-p

0.05

0 2001 2004 2007 2010 2013 2016 2019

ro

CHF

0 2001 2004 2007 2010 2013 2016 2019

of

USD 0.05

0 2001 2004 2007 2010 2013 2016 2019

0 2001 2004 2007 2010 2013 2016 2019

Jo

ur na

lP

re

Figure 1: Daily volatility series for top 12 currencies ranked by their averaged trading volumes per day during the sample period from 30 November 2000 to 15 February 2019. Notes: here presents volatility series ranging from 0 to 0.05 only for convenience of comparison, though the volatility of JPY, GBP, AUD, CHF, NZD and MXN exceeds 0.05 once or more.

36

of ro

1 0.9

-p

0.7 0.6

re

0.5 0.4 0.3 0.2 0.1 0 0.02

0.04

ur na

0

lP

Network Density(ND)

0.8

0.06

0.08

0.01

0.008 0.006 0.004

Global Efficiency(GE)

0.012

0.002 0 0.1

0.12

Threshold

Jo

Figure 2: Evolution of network density and global efficiency under various connectedness threshold levels.

37

of

CHF

CHF GNF

TRY

GNF

TRY CUP

CUP

BGN

BGN DKK

DKK

UGS

SEK

HUF

SEK

MAD

MAD HTG

CNY

EUR

IDR

QAR

CAD

GTQ

VND

NGN

KYD

MYR

PHP

PEN

BDT

USD AED

VND

INR

KRW

KYD

MYR

LAK THB

LKR

BDT

DZD PHP

PEN

CLP

CLP

NGN

GBP

ISK

LKR

DZD

GTQ

OMR

MXN

re

INR KRW

ECS

SGD

BRL

USD

GBP

ISK

SAR

PAB

SGD

AED

CNY QAR

AUD

ECS

OMR

HKD

EUR

ILS

SAR

MXN

-p

BHD HKD

BRL

JMD

TWD

BHD

ILS PAB

JPY

NZD

ZAR

AUD

KWD

XOF

JMD

TWD

IDR

LBP

BSD

KWD

BSD

CAD

CZK

LBP

XOF

KZT

HRK

NOK

PLN

CZK

JPY

NZD

ZAR

HTG

KZT HRK

NOK

PLN

UGS

ro

HUF

RON

RON

LAK THB

EGP

RUB

COP

lP

EGP TND

(a) Node size determined by out-degree

RUB

COP

TND

(b) Node size determined by in-degree

Jo

ur na

Figure 3: Snapshot of volatility connectedness network for 65 currencies in global forex marekts when the connectedness threshold is 0.01. Notes: the nodes’ size corresponds to currencies’ out-degree and in-degree in panels (a) and (b), respectively. The nodes’ color is set as pink for North American currencies; shallow green for European currencies; purple for Asian currencies; dark green for Oceanic currencies; blue for Latin American currencies; orange for African currencies; and gray for Middle East currencies. The edges’ direction is the same as that of corresponding volatility spillover, and the edges’ color follows their ending nodes and starting nodes respectively in panels (a) and (b).

38

Oceania

North America

of

Europe

ro

Asia

Middle East

Africa

-p

Latin America

85

ur na

System-wide Connectedness

90

lP

re

Figure 4: Snapshot of network connectedness across 7 regions. Note: node’s size is determined by its to-degree connectedness, edge’s color follows its start point, and edge’s width corresponds to the strength of the regional connectedness.

80

75

Jo

70

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Time

Figure 5: Rolling system-wide connectedness (i.e., total volatility connectedness) of 65 currencies. Note: the black line characterizes the smooth spline estimation of time-varying system-wide connectedness expressed in the green line.

39

of

From-degree connectedness

-p

re

ur na

lP

Currency

ro

USD PAB HKD BSD AED SAR OMR BHD CUP KYD VND ECS XOF EUR LBP QAR MXN RUB JPY COP ZAR KRW CAD AUD TRY NZD CLP ISK ILS DZD BRL GBP 2001 2002 2003 20042005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Time

Jo

Figure 6: Dynamic from-degree connectedness for the top and bottom 16 currencies ranked by the average strength of from-degree connectedness. Note: the colors from red to blue represent strengths from the highest to the lowest.

40

of

To-degree connectedness

-p

re

ur na

lP

Currency

ro

USD PAB BSD HKD AED SAR CUP BHD KYD OMR QAR VND ECS CNY XOF EUR PHP TRY AUD TND CAD ISK JPY UGS NZD BRL COP CLP KRW ILS GBP DZD 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

Time

Jo

Figure 7: Dynamic to-degree connectedness for the top and bottom 16 currencies ranked by the average strength of to-degree connectedness. Note: the colors from red to blue represent strengths from the highest to the lowest.

41

1.2 1 0.8 0.6

of

0.4 0.2 0

-0.2 -0.4 -0.6 -0.8

re

Time

-p

ro

Currency

Net-degree connectedness USD PAB BSD HKD AED CUP SAR QAR BHD KYD OMR VND ECS CNY XOF EUR NZD RON CAD SGD TWD INR PHP COP CLP JPY ILS GBP TND KRW UGS DZD 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

90

(a) H = 9 days, w = 90 days

70

90 80 70

2003 2006 2009 2012 2015 2018

90 80 70

(d) H = 12 days, w = 90 days

90

(e) H = 12 days, w = 120 days

Jo

80

2003 2006 2009 2012 2015 2018 90

70

2003 2006 2009 2012 2015 2018

(h) H = 15 days, w = 120 days

2003 2006 2009 2012 2015 2018 90

80

80

80

70

70

70

2003 2006 2009 2012 2015 2018

(f) H = 12 days, w = 150 days

80

70

90

(c) H = 9 days, w = 150 days

70

80

(g) H = 15 days, w = 90 days

90

2003 2006 2009 2012 2015 2018

2003 2006 2009 2012 2015 2018

90

(b) H = 9 days, w = 120 days

ur na

80

lP

Figure 8: Dynamic net-degree connectedness for top and bottom 16 currencies ranked by the average strength of net-degree connectedness. Note: the colors from red to blue represent strength from the highest to the lowest.

2003 2006 2009 2012 2015 2018

(i) H = 15 days, w = 150 days

2003 2006 2009 2012 2015 2018

Figure 9: Sensitivity of total volatility connectedness to forecast horizons H and window widths w.

42

(b) p = 2 days

90

80

80

80

70

70

70

(d) p = 4 days

90

2003 2006 2009 2012 2015 2018

(e) p = 5 days

90

80

80

70

70

(f) p = 6 days

90 80 70

2003 2006 2009 2012 2015 2018

2003 2006 2009 2012 2015 2018

-p

2003 2006 2009 2012 2015 2018

2003 2006 2009 2012 2015 2018

ro

2003 2006 2009 2012 2015 2018

(c) p = 3 days

90

of

(a) p = 1 days

90

re

Figure 10: Sensitivity of total volatility connectedness to VAR lags p.

80 70

(a) V abs

lP

90

ur na

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

(b) V sqrt

90 80 70

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

(c) V GARCH

Jo

90 80

70 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Figure 11: Sensitivity of total volatility connectedness to volatility estimators V .

43