## Abstract

We investigate the relation between trading activity—measured by the number of trades N_{Δt}—and the price change G_{Δt} 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_{Δt} in Δt and the variance (Formula Presented) of the price changes for all transactions in Δt. We find that N_{Δt} displays power-law decaying time correlations whereas W_{Δt} displays only weak time correlations, indicating that the long-range correlations previously found in |G_{Δt}| are largely due to those of N_{Δt}. Further, we analyse the distribution P{N_{Δt} > x} and find an asymptotic behaviour consistent with a power-law decay. We then argue that the tail-exponent of P{N_{Δt} > x} is insufficient to account for the tail-exponent of P{G_{Δt} > x}. Since N_{Δt} and W_{Δt} display only weak interdependence, we argue that the fat tails of the distribution P{G_{Δt} > x} arise from W_{Δt}, which has a distribution with power-law tail exponent consistent with our estimates for G_{Δt}. Further, we analyse the statistical properties of the number of shares Q_{Δt} traded in Δt, and find that the distribution of Q_{Δt} is consistent with a Lévy-stable distribution. We also quantify the relationship between Q_{Δt} and N_{Δt}, which provides one explanation for the previously observed volume–volatility co-movement.

Original language | English (US) |
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Pages (from-to) | 262-269 |

Number of pages | 8 |

Journal | Quantitative Finance |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Finance
- Economics, Econometrics and Finance(all)