Double Exponential Instability of Triangular Arbitrage Systems
AbstractIf financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1204.3422.
Date of creation: Apr 2012
Date of revision: Jun 2012
Publication status: Published in Discrete and Continuous Dynamical Systems Series B, Vol. 18, No. 2, 2013, pp. 349-376
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-23 (All new papers)
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- 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).
- Rod Cross & Victor Kozyakin & Brian O'Callaghan & Alexei Pokrovskii & Alexey Pokrovskiy, 2012. "Periodic Sequences Of Arbitrage: A Tale Of Four Currencies," Metroeconomica, Wiley Blackwell, vol. 63(2), pages 250-294, 05.
- Rod Cross & Victor Kozyakin & Brian O'Callaghan & Alexei Pokrovskii & Alexey Pokrovskiy, 2011. "Periodic Sequences of Arbitrage: A Tale of Four Currencies," Papers 1112.5850, arXiv.org.
- Rod Cross & Victor Kozyakin & Brian O'Callaghan & Alexei Pokrovskii & Alexey Pokrovskiy, 2010. "Periodic Sequences of Arbitrage: A Tale of Four Currencies," Working Papers 1019, University of Strathclyde Business School, Department of Economics.
- Rod Cross & Victor Kozyakin, 2012. "Fact and Fiction in FX Arbitrage Processes," Working Papers 1211, University of Strathclyde Business School, Department of Economics.
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