Double exponential instability of triangular arbitrage systems

Rod Cross; Victor Kozyakin

doi:10.3934/dcdsb.2013.18.349

Article Contents

2013, Volume 18, Issue 2: 349-376. Doi: 10.3934/dcdsb.2013.18.349

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Double exponential instability of triangular arbitrage systems

Rod Cross^1, and
Victor Kozyakin^2,

1.
Department of Economics, University of Strathclyde, Sir William Duncan Building, 130 Rottenrow, Glasgow G4 0GE
2.
Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane 19, Moscow 127994 GSP-4

Received: May 31, 2012

Revised: June 30, 2012

Published: February 2013

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Abstract

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 [18,9] 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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Mathematics Subject Classification: Primary: 91B26, 91B54, 91B64; Secondary: 15A60.

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