Long Memory and Fat Tails in Price Diffusion: Applications of Physics Thinking to Economics
Doyne Farmer
Santa Fe Institute
Although the random walk model originated as a model of price dynamics, and underlies the most important quantitative theories in financial economics, there is still very little understanding of what determines the diffusion rate of prices. The standard view is that it is determined by information arrival. In fact, recent evidence shows that it is driven by fluctuations in liquidity, i.e. in the availability of standing quotes that can be matched against new trading orders. I will present some alternative models for price diffusion and other important properties of markets, based on the idea that the diffusion rate of prices comes from the internal dynamics of liquidity. These models make use of physics-based methods, including dimensional analysis and mean field theory. I will also discuss the fat tails and long-memory of price fluctuations, and present preliminary models of their origin. All of this work is grounded in a study of a 350 million record data set from the London Stock Exchange.
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