Self-organization of price fluctuation distribution in evolving markets

Abstract

Financial markets can be seen as complex systems in non-equilibrium steady state, one of whose most important properties is the distribution of price fluctuations. Recently, there have been assertions that this distribution is qualitatively different in emerging markets as compared to developed markets. Here we analyse both high-frequency tick-by-tick as well as daily closing price data to show that the price fluctuations in the Indian stock market, one of the largest emerging markets, have a distribution that is identical to that observed for developed markets (e.g., NYSE). In particular, the cumulative distribution has a long tail described by a power law with an exponent $α\approx 3$. Also, we study the historical evolution of this distribution over the period of existence of the National Stock Exchange (NSE) of India, which coincided with the rapid transformation of the Indian economy due to liberalization, and show that this power law tail has been present almost throughout. We conclude that the ``inverse cubic law'' is a truly universal feature of a financial market, independent of its stage of development or the condition of the underlying economy.