|Title||Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study|
|Publication Type||Journal Article|
|Year of Publication||2007|
|Authors||C. A. Silva, and V. M. Yakovenko|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Keywords||2007, Single Fellow|
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.