Scaling and efficiency determine the irreversible evolution of a market

TL;DR

This paper introduces an analytical model for financial index evolution that incorporates market efficiency, scaling laws, and irreversibility, providing a reliable simulation method and insights into market dynamics.

Contribution

It presents a novel stochastic model that integrates empirical stylized facts, market efficiency constraints, and irreversibility to improve simulation accuracy of financial indices.

Findings

Model captures linear decorrelation of returns

Reproduces power-law volatility autocorrelation

Demonstrates predictive potential through simulation

Abstract

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. In addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model.