Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study
arXiv:physics/0608299 · doi:10.1016/j.physa.2007.03.051
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 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.
arXiv comment5 pages, 7 figures, RevTeX, proceedings of APFA-5. V.2: minor typos corrected, 2 references added
References in corpus (11)
- Scaling of the distribution of fluctuations of financial market indices
- Scaling of the distribution of price fluctuations of individual companies
- Fractional calculus and continuous-time finance II: the waiting-time distribution
- Economic Fluctuations and Diffusion
- A continuous time random walk model for financial distributions
- Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
- A study of the personal income distribution in Australia
- Scale-Dependent Price Fluctuations for the Indian Stock Market
- Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
- Inflation and deflation in stock markets
- On distribution of number of trades in different time windows in the stock market
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- Microscopic Origin of Non-Gaussian Distributions of Financial Returns
- A Model for Stock Returns and Volatility
- Combined Mutiplicative-Heston Model for Stochastic Volatility
- Renewal equations for option pricing
- Distributions of Historic Market Data - Stock Returns
- A contribution to the systematics of stochastic volatility models
- Maximum likelihood approach for several stochastic volatility models