Double Exponential Instability of Triangular Arbitrage Systems
If 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.
|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|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Rod Cross & Victor Kozyakin & Brian O'Callaghan & Alexei Pokrovskii & Alexey Pokrovskiy, 2012.
"Periodic Sequences Of Arbitrage: A Tale Of Four Currencies,"
Wiley Blackwell, vol. 63(2), pages 250-294, 05.
- 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.
- Cross, Rod & Kozyakin, Victor & Oâ€™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, 2011. "Periodic Sequences of Arbitrage: A Tale of Four Currencies," Papers 1112.5850, arXiv.org.