Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study

✍ Scribed by A. Christian Silva; Victor M. Yakovenko

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 459 KB
• Volume: 382
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2007.03.051

✦ Synopsis

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 non-trivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.