Multiplicative Stochastic Model of the Time Interval between Trades in Financial Markets

TL;DR

This paper introduces a multiplicative stochastic model for the time intervals between trades in financial markets, explaining spectral properties and power-law distributions of trading activity, highlighting the importance of transaction timing in market dynamics.

Contribution

The paper presents a novel multiplicative stochastic model that captures the spectral density and correlations of transaction counts, providing insights into the statistical properties of market activity.

Findings

Model reproduces spectral properties of real markets.

Explains power law distribution of trading activity.

Highlights the role of transaction timing in market fluctuations.

Abstract

Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely depend on the number of transactions. We introduce the multiplicative stochastic model of time interval between trades and analyze spectral density and correlations of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power law distribution of trading activity. Our study provides an evidence that statistical properties of financial markets are enclosed in the statistics of the time interval between trades. Multiplicative stochastic diffusion may serve as a consistent model for this statistics.