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If financial markets displayed the informational efficiency postulated in theefficient markets hypothesis (EMH), arbitrage operations would beself-extinguishing. The present paper considers arbitrage sequences in foreignexchange (FX) markets, in which trading platforms and information arefragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown thatsequences of triangular arbitrage operations in FX markets containing 4currencies and trader-arbitrageurs tend to display periodicity or growexponentially rather than being self-extinguishing. This paper extends theanalysis to 5 or higher-order currency worlds. The key findings are that in a5-currency world arbitrage sequences may also follow an exponential law as wellas display periodicity, but that in higher-order currency worlds a doubleexponential law may additionally apply. There is an "inheritance ofinstability" in the higher-order currency worlds. Profitable arbitrageoperations are thus endemic rather that displaying the self-extinguishingproperties implied by the EMH.

Double Exponential Instability of Triangular Arbitrage Systems