s . so c - ph ] 1 1 M ay 2 00 7 Self - organization of price fluctuation distribution in evolving mar - kets

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 ≈ 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. Introduction. – Financial markets are paradigmatic examples of complex systems, comprising a large number of interacting components that are subject to a constant flow of external information [1, 2]. Statistical physicists have studied simple interacting systems which self-organize into non-equilibrium steady states, often characterized by power law scaling [3]. Whether markets also show such behavior can be examined by looking for evidence of scaling functions which are invariant for different markets. The most prominent candidate for such an universal , scale-invariant property is the cumulative distribution of stock price fluctuations. The tails of this distribution has been reported to follow a power law, P c (x) ∼ x −α , with the exponent α ≈ 3 [4]. This " inverse cubic law " had been reported initially for a small number of stocks from the S&P 100 list [5]. Later, it was established from statistical analysis of stock returns in the German stock exchange [6], as well as for three major US markets, including the New York Stock Exchange (NYSE) [7]. The distribution was shown to be quite robust, retaining the same functional form for time scales of upto several days. Similar behavior has also been seen in the London Stock