## Abstract

We empirically quantify the relation between trading activity-measured by the number of transactions N-and the price change G(t) for a given stock, over a time interval [t,t+Δt]. We relate the time-dependent standard deviation of price changes-volatility-to two microscopic quantities: the number of transactions N(t) in Δt and the variance W^{2}(t) of the price changes for all transactions in Δt. We find that the long-ranged volatility correlations are largely due to those of N. We then argue that the tail-exponent of the distribution of N is insufficient to account for the tail-exponent of P{G > x}. Since N and W display only weak inter-dependency, our results show that the fat tails of the distribution P{G > x} arises from W, which has a distribution with power-law tail exponent consistent with our estimates for G.

Original language | English (US) |
---|---|

Pages (from-to) | 137-143 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 299 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2001 |

Event | Application of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic Duration: Feb 8 2001 → Feb 10 2001 |

## Keywords

- Anomalous diffusion
- Econophysics
- Stochastic volatility
- Subordinate processes

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics