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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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    File URL: http://hdl.handle.net/10943/177
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    4. Fisher,Franklin M., 1989. "Disequilibrium Foundations of Equilibrium Economics," Cambridge Books, Cambridge University Press, number 9780521378567, May.
    5. 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.
    6. 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.
    7. Shleifer, Andrei & Vishny, Robert W, 1997. " The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    8. 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.
    9. 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.
    10. Haskel, Jonathan & Wolf, Holger, 2001. " The Law of One Price--A Case Study," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(4), pages 545-558, December.
    11. 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.
    12. 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.
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    Citations

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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. 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. repec:ers:journl:v:xx:y:2017:i:2a:p:355-379 is not listed on IDEAS

    More about this item

    Keywords

    Four currencies; Limits to arbitrage; Recurrent sequences; Asynchronous systems;

    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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