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Periodic Sequences of Arbitrage: A Tale of Four Currencies

Author

Listed:
  • Rod Cross

    (Department of Economics, University of Strathclyde)

  • Victor Kozyakin

    (Institute for Information Transmission Problems, Russian Academy of Sciences,Bolshoj Karetny lane 19, Moscow 127994 GSP-4, Russia)

  • Brian O'Callaghan

    (Department of Applied Mathematics University College Cork, Ireland)

  • Alexei Pokrovskii

    (Department of Applied Mathematics University College Cork, Ireland)

  • Alexey Pokrovskiy

    (London School of Economics and Political Science)

Abstract

This paper investigates arbitrage chains involving four currencies and four foreign ex-change trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.

Suggested Citation

  • Rod Cross & Victor Kozyakin & Brian O'Callaghan & Alexei Pokrovskii & Alexey Pokrovskiy, 2010. "Periodic Sequences of Arbitrage: A Tale of Four Currencies," Working Papers 1019, University of Strathclyde Business School, Department of Economics.
    • Handle: RePEc:str:wpaper:1019
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    References listed on IDEAS

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    1. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    2. Fisher,Franklin M., 1989. "Disequilibrium Foundations of Equilibrium Economics," Cambridge Books, Cambridge University Press, number 9780521378567, September.
    3. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    4. Charles Engel, 1999. "Accounting for U.S. Real Exchange Rate Changes," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 507-538, June.
    5. Martin D. D. Evans & Richard K. Lyons, 2017. "How is Macro News Transmitted to Exchange Rates?," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 14, pages 547-596, World Scientific Publishing Co. Pte. Ltd..
    6. Osler, Carol L., 2005. "Stop-loss orders and price cascades in currency markets," Journal of International Money and Finance, Elsevier, vol. 24(2), pages 219-241, March.
    7. Maurice Obstfeld & Kenneth Rogoff, 2001. "The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 339-412, National Bureau of Economic Research, Inc.
    8. Shleifer, Andrei & Vishny, Robert W, 1997. "The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    9. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    10. Covrig, Vicentiu & Melvin, Michael, 2002. "Asymmetric information and price discovery in the FX market: does Tokyo know more about the yen?," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 271-285, August.
    11. Owen A. Lamont & Richard H. Thaler, 2003. "Anomalies: The Law of One Price in Financial Markets," Journal of Economic Perspectives, American Economic Association, vol. 17(4), pages 191-202, Fall.
    12. Kenneth A. Froot & Michael Kim & Kenneth Rogoff, 2019. "The Law of One Price Over 700 Years," Annals of Economics and Finance, Society for AEF, vol. 20(1), pages 1-35, May.
    13. Alan M. Taylor, 2002. "A Century Of Purchasing-Power Parity," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 139-150, February.
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    15. Deardorff, Alan V, 1979. "One-Way Arbitrage and Its Implications for the Foreign Exchange Markets," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 351-364, April.
    16. Rahi, Rohit & Zigrand, Jean-Pierre, 2008. "Arbitrage networks," LSE Research Online Documents on Economics 4787, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Alexander Mikhailovich Batkovskiy & Viktor Antonovich Nesterov & Olga Olegovna Reshetova & Elena Georgievna Semenova & Alena Vladimirovna Fomina, 2017. "Dynamic Model of Optimal Production Control in a Hysteretic Behaviour of Economic Agents," European Research Studies Journal, European Research Studies Journal, vol. 0(2A), pages 355-379.
    2. repec:edn:sirdps:378 is not listed on IDEAS
    3. Rod Cross & Victor Kozyakin, 2012. "Double Exponential Instability of Triangular Arbitrage Systems," Papers 1204.3422, arXiv.org, revised Jun 2012.
    4. Rod Cross & Victor Kozyakin, 2012. "Fact and Fiction in FX Arbitrage Processes," Working Papers 1211, University of Strathclyde Business School, Department of Economics.

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    More about this item

    Keywords

    Limits to arbitrage; Four currencies; Recurrent sequences; Asynchronous systems;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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