Speculation and Power Law

TL;DR

This paper explains the universal power law distribution of financial price changes through a simple feedback mechanism inherent in speculation, modeled as a random coefficient autoregressive process, providing a fundamental understanding of market dynamics.

Contribution

It introduces a straightforward principle linking speculation feedback to power law distributions, offering a new theoretical explanation for observed market regularities.

Findings

Financial price changes follow a power law with a cubic exponent.

The feedback mechanism in speculation leads to a random coefficient autoregressive process.

Power law distribution is derived using Kesten's theorem.

Abstract

It is now well established empirically that financial price changes are distributed according to a power law, with cubic exponent. This is a fascinating regularity, as it holds for various classes of securities, on various markets, and on various time scales. The universality of this law suggests that there must be some basic, general and stable mechanism behind it. The standard (neoclassical) paradigm implies no such mechanism. Agent-based models of financial markets, on the other hand, exhibit realistic price changes, but they involve relatively complicated, and often mathematically intractable, mechanisms. This paper identifies a simple principle behind the power law: the feedback intrinsic to the very idea of speculation, namely buying when one expects a price rise (and selling when one expects a price fall). By this feedback, price changes follow a random coefficient autoregressive process, and therefore they have a power law by Kesten theorem.