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Periodic Sequences of Arbitrage: A Tale of Four Currencies

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  • Cross, Rod
  • Kozyakin, Victor
  • O’Callaghan, Brian
  • Pokrovskii, Alexei
  • Pokrovskiy, Alexey

Abstract

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we fi nd 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

  • Cross, Rod & Kozyakin, Victor & O’Callaghan, Brian & Pokrovskii, Alexei & Pokrovskiy, Alexey, 2010. "Periodic Sequences of Arbitrage: A Tale of Four Currencies," SIRE Discussion Papers 2010-66, Scottish Institute for Research in Economics (SIRE).
    • Handle: RePEc:edn:sirdps:177
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    2. Fisher,Franklin M., 1989. "Disequilibrium Foundations of Equilibrium Economics," Cambridge Books, Cambridge University Press, number 9780521378567, September.
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    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.
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    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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    Cited by:

    1. Rod Cross & Victor Kozyakin, 2012. "Fact and Fiction in FX Arbitrage Processes," Working Papers 1211, University of Strathclyde Business School, Department of Economics.
    2. 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.
    3. repec:edn:sirdps:378 is not listed on IDEAS
    4. Rod Cross & Victor Kozyakin, 2012. "Double Exponential Instability of Triangular Arbitrage Systems," Papers 1204.3422, arXiv.org, revised Jun 2012.

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    More about this item

    Keywords

    Four currencies; Limits to arbitrage; 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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