Complexity, Financial Markets and their Scaling Laws

Indranil Mukherjee and Amitava Sarkar

DEGIT Conference Papers from DEGIT, Dynamics, Economic Growth, and International Trade

Abstract: This paper attempts to analyze financial markets characterized by, among others, by stability or the lack of it, or more directly volatility, in the framework of complexity. The seemingly uncorrelated swings of financial indices and the extreme event of a crash constitute typical phenomena of complex systems. The financial market dynamics is sometimes described using terminology from the theory of turbulence, while the financial crash is compared with a phase transition of a physical many-body system. It is possible to identify indicators for nonlinearity in financial markets, such as speculative bubbles. One also notes how quickly panic can spread in case of larger losses. These phenomena are examples of typical nonlinear processes called autocatalytic, which are characterized by conditions in which small stimuli can be strongly amplified due to the internal dynamics of the system. Financial markets can be regarded as “model” complex systems which are evolving continuously and generate huge amounts of data. It is discussed how the properties of financial markets correspond to those of a complex system. The different levels of complexity present in a financial market and the collective behaviour emerging from these markets, regarded as some kind of dynamical systems, are analyzed. The concept of auto-catalyticity is invoked to describe the power-law behaviour operating in financial markets. The concept of scaling is examined and the different scaling laws occurring in finance are discussed. Multi-fractal models of asset returns are introduced and their importance emphasized. An overview of complex systems at the beginning is provided in order to develop the concepts necessary to examine financial markets under the lens of complexity.

Pages: 17 pages JEL Classification:
Date: 2011-09
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