三角套利系统的双指数不稳定性
Double Exponential Instability of Triangular Arbitrage Systems
摘要：
如果金融市场表现出有效市场假说（EMH）中假设的信息效率，那么套利操作将自我熄灭。本文研究了外汇（FX）市场中的套利序列，其中交易平台和信息是分散的。Kozyakin等人（2010）和Cross等人（2012）的研究表明，在包含4种货币和交易员-仲裁员的外汇市场中，三角套利操作的序列往往显示出周期性或指数增长，而不是自我熄灭。本文将分析扩展到5个或更高阶的货币世界。关键的发现是，在5种货币的世界中，套利序列也可能遵循指数规律并显示周期性，但在更高阶的货币世界中，双指数规律可能也适用。在更高层次的货币世界中，存在着一种“不稳定性的遗传”。因此，有利可图的套利操作是地方性的，而不是表现出有效市场假说所暗示的自熄特性。
英文摘要：
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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