Inverse cubic law of index fluctuation distribution in Indian markets

Abstract

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, e.g., the New York Stock Exchange (NYSE) have been found to show heavy-tailed return distribution with a characteristic power-law exponent, the universality of such behavior has been debated, particularly in regard to emerging markets. 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 tick-by-tick data from the National Stock Exchange (NSE), as well as, daily closing data from both NSE and Bombay Stock Exchange (BSE). We find that the cumulative distributions of index returns have long tails consistent with a power-law having exponent \alpha \approx 3, at time-scales of both 1 min and 1 day. This ``inverse cubic law'' is quantitatively similar to what has been observed in developed markets, thereby providing strong evidence of universality in the behavior of market fluctuations.