Chapter 1
Introduction
There is an extensive literature of analogies between physical and economic systems. Among these is the analogy between physical systems exhibiting critical phenomena and the stock market. This analogy has also been discussed bypopularacademics: NiallFerguson,thecontroversialeconomichistorian,usedtheanalogytofurtheranargument againstfinancialregulation[14]. MalcolmGladwell’sbestsellingbookThe Tipping Point [17]couldeasilyberetitled The Critical Point. Beyond stock markets, the theory has been extended to many other fields, including virus dynamics, ecological shifts, and traffic jams [45]. With this burgeoning amount of literature, one must be careful that the aesthetic appeal of the analogy does not substitute for a theoretically solid and empirically verified analysis of its validity. Indeed, we need to see if market crashes can be thought of within any kind of universal framework, since, if not, any empirical description seems hopeless. The purpose of this thesis is, then, to critique the analogy between critical systems and stock markets. It is the contention of this thesis that the aforementioned analogy has some validity, but important physics has thus far been neglected. Our means of performing the analysis will be to examine the correlation properties of minute-by-minute stock market data. These results will be compared to a generic condensed matter system, the Ising model, which is a simple and well-studied model of ferromagnetism that exhibits a phase transition in certain dimensions. Our primary result is that stock market crashes provide a unique opportunity to study the “spatial structure” of the stock market, which we find to lack an obvious measure of distance. This leads us to propose a condensed matter system that has similar properties, a zero dimensional Ising model, which similarly has no spatial structure. We will then show that the zero dimensional Ising model does not, strictly speaking, exhibit a phase transition, although it does exhibit something similar to it.
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