Contagion in the world's stock exchanges seen as a set of coupled oscillators

We study how the phenomenon of contagion can take place in the network of the world's stock exchanges when each stock exchange acts as an integrate-and-fire oscillator. The characteristic non-linear price behavior of integrate-and-fire oscillators is supported by empirical data and has a behavioral origin called change-blindness. One advantage of the integrate-and-fire dynamics is that it enables a direct identification of cause and effect in price movements, without the need for statistical tests such as Granger causality tests, often used in the identification of causes of contagion. Our methodology can thereby identify the most relevant nodes with respect to onset of contagion in the network of stock exchanges, as well as identify potential periods of high vulnerability of the network. Over the time period of study, our method is able to identify the importance of the U.K. and U.S. markets as sources for propagation of positive returns, whereas, more surprisingly, the Swiss and some Asian markets (China, South Korea) seem to play a particular role with respect to propagation of downturns across markets. The model is characterized by a separation of time scales, brought about by a slow build-up of stresses, for example, due to (say monthly/yearly) macroeconomic factors, and then a fast (say hourly/daily) release of stresses through “price-quakes” in price movements across the world's network of stock exchanges.