This paper investigates arbitrage chains involving d currencies and d foreign exchange trader-arbitrageurs. The commonly recognized belief in economics and finance is that arbitrage has the effect of causing prices in different marketsto converge. This conjecture was recently disproved in Kozyakin et al. (2010) ; Cross et al. (2012) , where was shown that for the case of four currencies arbitrage chains may be periodic or exponentially unstable. In contrast with the four-currency case, we find that arbitrage operations when d >= 5 currencies are present may appear very unstable, with the exchange rates growing in accordance with the double exponential law !
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.
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This paper investigates arbitrage chains involving d currencies and d foreign exchange trader-arbitrageurs. The commonly recognized belief in economics and finance is that arbitrage has the effect of causing prices in different marketsto converge. This conjecture was recently disproved in
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
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for the case of four currencies arbitrage chains may be periodic or exponentially unstable. In contrast with the four-currency case, we find that arbitrage operations when d >=
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
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currencies are present may appear very unstable, with the exchange rates growing in accordance with the
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
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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.