Collaborative Research: Understanding Large Movements in Stock Market Activity

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The basic motivation of this investigation is to understand the power-law distributions that describe various properties characterizing large movements in stock price fluctuations, with characteristic exponents that seem to be universal for different sizes of stocks and different stock markets around the world. This project develops a model of the microbehavior of financial markets to account for these empirically observed facts. The model will have the following key components: (a) market participants behave strategically, i.e., they seek to minimize execution time and price impact, and (b) the size distribution of mutual funds has a power law tail with exponent 1. The model is tested for consistency with a series of equal-time codependences among return, volume, and number of trades that are displayed by empirical data. This project consolidates and extends the conceptual framework of the model in several directions. The model predicts that some mechanisms proposed to reduce extreme fluctuations are ineffective. For example, a Tobin tax and circuit breakers do not change the value of the exponent of returns, but a modified Tobin tax whose tax rate increases sufficiently quickly with volume traded decreases the fatness of the return distribution. The model also suggests a way to use volume to parse out noise from news in return fluctuations, and this project explores how useful this approach is. Volatility is known to be autocorrelated, and preliminary evidence suggests that number of trades and return volatility are similarly autocorrelated. Their long-term memory exponents are very close. The investigators study the propagation of volatility, volume and number of trades in a systematic way, particularly focusing on the extreme events and the long-term memory properties. This study achieves a reasonably complete description of the way market activity is created and propagates.