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Periodic Sequences of Arbitrage: A Tale of Four Currencies

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Author Info

  • 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.

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Bibliographic Info

Paper provided by University of Strathclyde Business School, Department of Economics in its series Working Papers with number 1019.

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Length: 31 pages
Date of creation: Oct 2010
Date of revision:
Handle: RePEc:str:wpaper:1019

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

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  1. Jonathan Haskel & Holger Wolf, 2001. "The Law of One Price - A Case Study," NBER Working Papers 8112, National Bureau of Economic Research, Inc.
  2. Shleifer, Andrei & Vishny, Robert W, 1997. " The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
  3. 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 453-75, July.
  4. Alan M. Taylor, 2000. "A Century of Purchasing-Power Parity," NBER Working Papers 8012, National Bureau of Economic Research, Inc.
  5. Charles Engel & Kenneth D. West, 2004. "Exchange Rates and Fundamentals," NBER Working Papers 10723, National Bureau of Economic Research, Inc.
  6. Engel, C., 1996. "Accounting for U.S. Real Exchange Rate Changes," Discussion Papers in Economics at the University of Washington 96-02, Department of Economics at the University of Washington.
  7. 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.
  8. C. L. Osler, 2002. "Stop-loss orders and price cascades in currency markets," Staff Reports 150, Federal Reserve Bank of New York.
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Cited by:
  1. Rod Cross & Victor Kozyakin, 2014. "Fact and fictions in FX arbitrage processes," Working Papers 1403, University of Strathclyde Business School, Department of Economics.
  2. Rod Cross & Victor Kozyakin, 2012. "Double Exponential Instability of Triangular Arbitrage Systems," Papers 1204.3422, arXiv.org, revised Jun 2012.

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