Inverse cubic law of index fluctuation distribution in Indian markets

One of the principal statistical features characterizing the activity in financial markets is the distribution of fluctuations in market indicators such as the index. While the developed stock markets such as the New York Stock Exchange (NYSE) have been found to show heavy-tailed fluctuation distribution, there have been claims that emerging markets behave differently. Here we investigate the distribution of several indices from the Indian financial market, one of the largest emerging markets in the world. We have used both tick-by-tick data from the National Stock Exchange (NSE) and daily closing data from both NSE and Bombay Stock Exchange (BSE). We find that the cumulative distribution of index fluctuations has long tails consistent with a power law having exponent α ≈ 3, independent of the time-scale of observation or the market index used for the analysis. This “inverse cubic law” is quantitatively similar to what has been observed in developed markets, thereby providing strong evidence that, at least in terms of fluctuations, these markets behave similarly. PACS. 89.65.Gh Economics; econophysics, financial markets, business and management – 05.40.Fb Random walks and Levy flights