Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study
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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 Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.
5 pages, 7 figures, RevTeX, proceedings of APFA-5. V.2: minor typos corrected, 2 references added
5 pages, 7 figures, RevTeX, proceedings of APFA-5. V.2: minor typos corrected, 2 references added