IDEAS home Printed from https://ideas.repec.org/p/edn/sirdps/177.html
   My bibliography  Save this paper

Periodic Sequences of Arbitrage: A Tale of Four Currencies

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10943/177
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, June.
    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.
    14. Jonathan Haskel & Holger Wolf, 2001. "The Law of One Price—A Case Study," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(4), pages 545-558, December.
    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.
    17. repec:bla:scandj:v:103:y:2001:i:4:p:545-58 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    2. Hai Long Vo & Duc Hong Vo, 2023. "The purchasing power parity and exchange‐rate economics half a century on," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 446-479, April.
    3. King, Michael R. & Osler, Carol L. & Rime, Dagfinn, 2013. "The market microstructure approach to foreign exchange: Looking back and looking forward," Journal of International Money and Finance, Elsevier, vol. 38(C), pages 95-119.
    4. Enrique Martínez García, 2008. "Globalization and monetary policy: an introduction," Globalization Institute Working Papers 11, Federal Reserve Bank of Dallas.
    5. Balázs Égert & László Halpern & Ronald MacDonald, 2006. "Equilibrium Exchange Rates in Transition Economies: Taking Stock of the Issues," Journal of Economic Surveys, Wiley Blackwell, vol. 20(2), pages 257-324, April.
    6. Cross, Rod & Kozyakin, Victor, 2012. "Fact And Fiction In FX Arbitrage Processes," SIRE Discussion Papers 2012-86, Scottish Institute for Research in Economics (SIRE).
    7. Crucini, Mario J. & Shintani, Mototsugu, 2008. "Persistence in law of one price deviations: Evidence from micro-data," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 629-644, April.
    8. Engel, Charles, 2014. "Exchange Rates and Interest Parity," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 453-522, Elsevier.
    9. Emmanuel Farhi & Xavier Gabaix, "undated". "Rare Disasters and Exchange Rates," Working Paper 71001, Harvard University OpenScholar.
    10. Lucio Sarno, 2005. "Viewpoint: Towards a solution to the puzzles in exchange rate economics: where do we stand?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(3), pages 673-708, August.
    11. Carol L. Osler, 2006. "Macro lessons from microstructure," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 11(1), pages 55-80.
    12. Michael Fidora & Claire Giordano & Martin Schmitz, 2021. "Real Exchange Rate Misalignments in the Euro Area," Open Economies Review, Springer, vol. 32(1), pages 71-107, February.
    13. repec:edn:sirdps:378 is not listed on IDEAS
    14. Stijn Claessens & M Ayhan Kose, 2018. "Frontiers of macrofinancial linkages," BIS Papers, Bank for International Settlements, number 95.
    15. repec:onb:oenbwp:y::i:106:b:1 is not listed on IDEAS
    16. Peltonen, Tuomas A. & Sager, Michael, 2009. "Productivity shocks and real exchange rate: a reappraisal," Working Paper Series 1046, European Central Bank.
    17. Rabanal, Pau & Rubio-Ramírez, Juan F., 2015. "Can international macroeconomic models explain low-frequency movements of real exchange rates?," Journal of International Economics, Elsevier, vol. 96(1), pages 199-211.
    18. Candian, Giacomo, 2019. "Information frictions and real exchange rate dynamics," Journal of International Economics, Elsevier, vol. 116(C), pages 189-205.
    19. DavidC. Parsley & Shang-Jin Wei, 2007. "A Prism into the PPP Puzzles: The Micro-Foundations of Big Mac Real Exchange Rates," Economic Journal, Royal Economic Society, vol. 117(523), pages 1336-1356, October.
    20. Astorga, Pablo, 2012. "Mean reversion in long-horizon real exchange rates: Evidence from Latin America," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1529-1550.
    21. Domenico Delli Gatti & Tommaso Ferraresi & Filippo Gusella & Lilit Popoyan & Giorgio Ricchiuti & Andrea Roventini, 2024. "The interplay between real and exchange rate market: an agent-based model approach," Working Papers - Economics wp2024_10.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    22. Javier Bianchi & Saki Bigio & Charles Engel, 2021. "Scrambling for Dollars: International Liquidity, Banks and Exchange Rates," Working Papers 786, Federal Reserve Bank of Minneapolis.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:edn:sirdps:177. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Research Office (email available below). General contact details of provider: https://edirc.repec.org/data/sireeuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.