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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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    3. Rod Cross & Victor Kozyakin, 2012. "Double Exponential Instability of Triangular Arbitrage Systems," Papers 1204.3422, arXiv.org, revised Jun 2012.
    4. Rod Cross & Victor Kozyakin, 2012. "Fact and Fiction in FX Arbitrage Processes," Working Papers 1211, University of Strathclyde Business School, Department of Economics.
    5. 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.

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    Keywords

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    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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