Scale-Dependent Price Fluctuations for the Indian Stock Market

Abstract

Classic studies of the probability density of price fluctuations $g$ for stocks and foreign exchanges of several highly developed economies have been interpreted using a {\it power-law} probability density function $P(g) \sim g^{-(α+1)}$ with exponent values $α> 2$, which are outside the Lévy-stable regime $0 < α< 2$. To test the universality of this relationship for less highly developed economies, we analyze daily returns for the period Nov. 1994--June 2002 for the 49 largest stocks of the National Stock Exchange which has the highest volume of trade in India. We find that $P(g)$ decays as an {\it exponential} function $P(g) \sim \exp(-βg)$ with a characteristic decay scales $β= 1.51 \pm 0.05$ for the negative tail and $β= 1.34 \pm 0.04$ for the positive tail, which is significantly different from that observed for developed economies. Thus we conclude that the Indian stock market may belong to a universality class that differs from those of developed countries analyzed previously.