Scaling and efficiency determine the irreversible evolution of a market

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.

5 pages, 4 figures

References in corpus (3)

• Crackling Noise
• Renormalization Group and Probability Theory
• Central limit theorem for anomalous scaling due to correlations

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• Minimal Agent Based Model for Financial Markets I: Origin and Self-Organization of Stylized Facts
• Emergence of universal scaling in financial markets from mean-field dynamics
• Opinion Dynamics in Financial Markets via Random Networks
• Modeling the non-Markovian, non-stationary scaling dynamics of financial markets
• Anomalous scaling due to correlations: Limit theorems and self-similar processes
• Scaling symmetry, renormalization, and time series modeling
• Role of scaling in the statistical modeling of finance
• Multiplicative noise, fast convolution, and pricing
• Option pricing with non-Gaussian scaling and infinite-state switching volatility
• Aftershock prediction for high-frequency financial markets' dynamics