Scaling and efficiency determine the irreversible evolution of a market

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 104; no. 50; pp. 19741 - 19744
• Main Authors: Baldovin, F, Stella, A.L
• Format: Journal Article
• Language: English
• Published: Washington National Academy of Sciences 11.12.2007; National Acad Sciences
• Subjects: Autocorrelation; Central limit theorem; Complex systems; Economics; Efficiency; Efficient markets; Market analysis; Mathematical moments; Modeling; Physical Sciences; Power laws; Simulations; Social Sciences; Stochastic models; Stochastic processes; Time dependence; Time series
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0706046104

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.