Blackett Laboratory, Imperial College London, London, England, United Kingdom.
Center for Complexity Science, Imperial College London, London, England, United Kingdom.
PLoS One. 2020 Jun 24;15(6):e0234709. doi: 10.1371/journal.pone.0234709. eCollection 2020.
Foreign exchange rates movements exhibit significant cross-correlations even on very short time-scales. The effect of these statistical relationships become evident during extreme market events, such as flash crashes. Although a deep understanding of cross-currency correlations would be clearly beneficial for conceiving more stable and safer foreign exchange markets, the microscopic origins of these interdependencies have not been extensively investigated. This paper introduces an agent-based model which describes the emergence of cross-currency correlations from the interactions between market makers and an arbitrager. The model qualitatively replicates the time-scale vs. cross-correlation diagrams observed in real trading data, suggesting that triangular arbitrage plays a primary role in the entanglement of the dynamics of different foreign exchange rates. Furthermore, the model shows how the features of the cross-correlation function between two foreign exchange rates, such as its sign and value, emerge from the interplay between triangular arbitrage and trend-following strategies. In particular, the interaction of these trading strategies favors certain combinations of price trend signs across markets, thus altering the probability of observing two foreign exchange rates drifting in the same or opposite direction. Ultimately, this entangles the dynamics of foreign exchange rate pairs, leading to cross-correlation functions that resemble those observed in real trading data.
汇率变动即使在很短的时间尺度上也表现出显著的交叉相关性。在极端市场事件（如闪崩）期间，这些统计关系的影响变得明显。尽管深入了解交叉货币相关性显然有助于构建更稳定、更安全的外汇市场，但这些相关性的微观起源尚未得到广泛研究。本文引入了一个基于代理的模型，该模型描述了做市商和套利者之间的相互作用如何导致交叉货币相关性的出现。该模型定性地复制了在真实交易数据中观察到的时间尺度与交叉相关性图，表明三角套利在不同外汇汇率动态的纠缠中起着主要作用。此外，该模型还展示了两种外汇汇率之间的交叉相关函数的特征（如符号和值）如何从三角套利和趋势跟踪策略之间的相互作用中出现。特别是，这些交易策略的相互作用有利于市场间价格趋势符号的某些组合，从而改变观察两种外汇汇率朝着相同或相反方向漂移的概率。最终，这会使外汇汇率对的动态纠缠在一起，导致类似于真实交易数据中观察到的交叉相关函数。
