Continuous-Time Random Walk with multi-step memory: An application to market dynamics

TL;DR

This paper introduces an analytically solvable continuous-time random walk model with multi-step memory, capturing dependencies in market price jumps, validated against high-frequency trading data and bid-ask bounce mechanisms.

Contribution

It develops a novel CTRW model incorporating multi-step memory, extending the formalism's ability to analyze market dynamics with empirical validation.

Findings

Model accurately reproduces empirical velocity autocorrelation functions.

Incorporates bid-ask bounce mechanism to explain market microstructure effects.

Extends CTRW formalism with exact analytical solutions.

Abstract

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.