Article ID Journal Published Year Pages File Type
979601 Physica A: Statistical Mechanics and its Applications 2007 8 Pages PDF
Abstract

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N   for a given time interval ΔtΔt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N  . Combining these two distributions produces a non-trivial distribution of log-returns for a given time interval ΔtΔt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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