Double Exponential Instability of Triangular Arbitrage Systems

Details Double Exponential Instability of Triangular Arbitrage Systems Double Exponential Instability of Triangular Arbitrage Systems

2012-04-16

arxiv.org/abs/1204.3422v2

Economy

Quantitative Finance

General Finance

19 pages, 6 bibliography references

Scientific paper

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 markets to 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!

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