IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0234709.html
   My bibliography  Save this article

The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets

Author

Listed:
  • Alberto Ciacci
  • Takumi Sueshige
  • Hideki Takayasu
  • Kim Christensen
  • Misako Takayasu

Abstract

Foreign exchange rates movements exhibit significant cross-correlations even on very short time-scales. The effect of these statistical relationships become evident during extreme market events, such as flash crashes. Although a deep understanding of cross-currency correlations would be clearly beneficial for conceiving more stable and safer foreign exchange markets, the microscopic origins of these interdependencies have not been extensively investigated. This paper introduces an agent-based model which describes the emergence of cross-currency correlations from the interactions between market makers and an arbitrager. The model qualitatively replicates the time-scale vs. cross-correlation diagrams observed in real trading data, suggesting that triangular arbitrage plays a primary role in the entanglement of the dynamics of different foreign exchange rates. Furthermore, the model shows how the features of the cross-correlation function between two foreign exchange rates, such as its sign and value, emerge from the interplay between triangular arbitrage and trend-following strategies. In particular, the interaction of these trading strategies favors certain combinations of price trend signs across markets, thus altering the probability of observing two foreign exchange rates drifting in the same or opposite direction. Ultimately, this entangles the dynamics of foreign exchange rate pairs, leading to cross-correlation functions that resemble those observed in real trading data.

Suggested Citation

  • Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    • Handle: RePEc:plo:pone00:0234709
    DOI: 10.1371/journal.pone.0234709
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0234709
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0234709&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0234709?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yamada, Kenta & Takayasu, Hideki & Takayasu, Misako, 2007. "Characterization of foreign exchange market using the threshold-dealer-model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 340-346.
    2. Luisanna Cocco & Giulio Concas & Michele Marchesi, 2017. "Using an artificial financial market for studying a cryptocurrency market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(2), pages 345-365, July.
    3. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543540, HAL.
    4. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    5. Aiba, Yukihiro & Hatano, Naomichi, 2006. "A microscopic model of triangular arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 572-584.
    6. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543547, HAL.
    7. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    8. Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
    9. Foucault, Thierry, 1999. "Order flow composition and trading costs in a dynamic limit order market1," Journal of Financial Markets, Elsevier, vol. 2(2), pages 99-134, May.
    10. Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 346-353.
    11. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    12. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543545, HAL.
    13. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    14. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    15. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    16. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    17. Chakravarty Sugato & Holden Craig W., 1995. "An Integrated Model of Market and Limit Orders," Journal of Financial Intermediation, Elsevier, vol. 4(3), pages 213-241, July.
    18. Ilija Zovko & J Doyne Farmer, 2002. "The power of patience: a behavioural regularity in limit-order placement," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 387-392.
    19. Bonart, Julius & Lillo, Fabrizio, 2018. "A continuous and efficient fundamental price on the discrete order book grid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 698-713.
    20. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    21. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    22. J. Doyne Farmer & Martin Shubik & Eric Smith, 2005. "Economics: the next physical science?," Cowles Foundation Discussion Papers 1520, Cowles Foundation for Research in Economics, Yale University.
    23. Gao-Feng Gu & Wei-Xing Zhou, 2008. "Emergence of long memory in stock volatility from a modified Mike-Farmer model," Papers 0807.4639, arXiv.org, revised May 2009.
    24. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
    25. Yukihiro Aiba & Naomichi Hatano & Hideki Takayasu & Kouhei Marumo & Tokiko Shimizu, 2002. "Triangular arbitrage as an interaction among foreign exchange rates," Papers cond-mat/0202391, arXiv.org, revised Mar 2002.
    26. Roman Kozhan & Wing Wah Tham, 2012. "Execution Risk in High-Frequency Arbitrage," Management Science, INFORMS, vol. 58(11), pages 2131-2149, November.
    27. Takayasu, Hideki & Miura, Hitoshi & Hirabayashi, Tadashi & Hamada, Koichi, 1992. "Statistical properties of deterministic threshold elements — the case of market price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(1), pages 127-134.
    28. Aiba, Yukihiro & Hatano, Naomichi & Takayasu, Hideki & Marumo, Kouhei & Shimizu, Tokiko, 2002. "Triangular arbitrage as an interaction among foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 467-479.
    29. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    30. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    31. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543546, HAL.
    32. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    33. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    34. Dagfinn Rime & Andreas Schrimpf, 2013. "The anatomy of the global FX market through the lens of the 2013 Triennial Survey," BIS Quarterly Review, Bank for International Settlements, December.
    35. Damien Challet & Robin Stinchcombe, 2003. "Non-constant rates and over-diffusive prices in a simple model of limit order markets," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 155-162.
    36. Daniel J. Fenn & Sam D. Howison & Mark Mcdonald & Stacy Williams & Neil F. Johnson, 2009. "The Mirage Of Triangular Arbitrage In The Spot Foreign Exchange Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1105-1123.
    37. Y. Aiba & N. Hatano, 2006. "A microscopic model of triangular arbitrage," Papers physics/0602171, arXiv.org.
    38. Kiyoshi Kanazawa & Takumi Sueshige & Hideki Takayasu & Misako Takayasu, 2017. "Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders," Papers 1703.06739, arXiv.org, revised Mar 2018.
    39. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
    40. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven Markets," Working Papers hal-00515891, HAL.
    41. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543544, HAL.
    42. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    43. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    44. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    45. Mr. Fei Han & Mr. Niklas J Westelius, 2019. "Anatomy of Sudden Yen Appreciations," IMF Working Papers 2019/136, International Monetary Fund.
    46. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
    47. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    48. Ioanid Rosu, 2010. "Liquidity and Information in Order Driven markets," Post-Print hal-00543541, HAL.
    49. F. Lillo, 2007. "Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(4), pages 453-459, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    2. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    3. Alessio Emanuele Biondo, 2020. "Information versus imitation in a real-time agent-based model of financial markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 613-631, July.
    4. Biondo, Alessio Emanuele, 2017. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics Discussion Papers 2017-104, Kiel Institute for the World Economy (IfW Kiel).
    5. Frank McGroarty & Ash Booth & Enrico Gerding & V. L. Raju Chinthalapati, 2019. "High frequency trading strategies, market fragility and price spikes: an agent based model perspective," Annals of Operations Research, Springer, vol. 282(1), pages 217-244, November.
    6. Dugast, J., 2013. "Limited attention and news arrival in limit order markets," Working papers 449, Banque de France.
    7. Kozhan, Roman & Salmon, Mark, 2012. "The information content of a limit order book: The case of an FX market," Journal of Financial Markets, Elsevier, vol. 15(1), pages 1-28.
    8. Zihao Zhang & Stefan Zohren & Stephen Roberts, 2018. "DeepLOB: Deep Convolutional Neural Networks for Limit Order Books," Papers 1808.03668, arXiv.org, revised Jan 2020.
    9. Ningyuan Chen & Steven Kou & Chun Wang, 2018. "A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure," Management Science, INFORMS, vol. 64(2), pages 784-803, February.
    10. Alessio Emanuele Biondo, 2018. "Order book microstructure and policies for financial stability," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 35(1), pages 196-218, March.
    11. Jiahua Wang & Hongliang Zhu & Dongxin Li, 2018. "Price Dynamics in an Order-Driven Market with Bayesian Learning," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    12. Fa-Bin Shi & Xiao-Qian Sun & Jin-Hua Gao & Li Xu & Hua-Wei Shen & Xue-Qi Cheng, 2019. "Anomaly detection in Bitcoin market via price return analysis," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-11, June.
    13. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    14. Yiqi Liu & Qiang Liu & Zhi Liu & Deng Ding, 2017. "Determining the integrated volatility via limit order books with multiple records," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1697-1714, November.
    15. Hautsch, Nikolaus & Huang, Ruihong, 2012. "The market impact of a limit order," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 501-522.
    16. Yosra Mefteh Rekik & Younes Boujelbene, 2015. "Price Dynamics and Market Volatility: Behavioral Heterogeneity under Switching Trading Strategies on Artificial Financial Market," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 6(2), pages 33-43, April.
    17. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    18. Ingrid Lo & Stephen Sapp, 2011. "Belief Dispersion and Order Submission Strategies in the Foreign Exchange Market," Staff Working Papers 11-8, Bank of Canada.
    19. Hai-Chuan Xu & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou & H Eugene Stanley, 2016. "Limit-order book resiliency after effective market orders: Spread, depth and intensity," Papers 1602.00731, arXiv.org, revised Feb 2017.
    20. Danny Lo, 2015. "Essays in Market Microstructure and Investor Trading," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2015.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0234709. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.