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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.

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File URL: http://repo.sire.ac.uk/handle/10943/177
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Bibliographic Info

Paper provided by Scottish Institute for Research in Economics (SIRE) in its series SIRE Discussion Papers with number 2010-66.

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Date of creation: 2010
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Handle: RePEc:edn:sirdps:177

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

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References

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  1. Charles Engel & Kenneth D. West, 2003. "Exchange rates and fundamentals," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  2. Alan M. Taylor, 2000. "A Century of Purchasing-Power Parity," NBER Working Papers 8012, National Bureau of Economic Research, Inc.
  3. Charles Engel, 1995. "Accounting for U.S. Real Exchange Rate Changes," NBER Working Papers 5394, National Bureau of Economic Research, Inc.
  4. Haskel, Jonathan & Wolf, Holger, 2001. " The Law of One Price--A Case Study," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(4), pages 545-58, December.
  5. Andrei Shleifer ad Robert W. Vishny, 1995. "The Limits of Arbitrage," Harvard Institute of Economic Research Working Papers 1725, Harvard - Institute of Economic Research.
  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. 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. 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.
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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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