Stochastic model of financial markets reproducing scaling and memory in volatility return intervals

V. Gontis, S. Havlin, A. Kononovicius, B. Podobnik, H. E. Stanley

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.

Original languageEnglish
Pages (from-to)1091-1102
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 15 Nov 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


The Boston University work was supported by NSF Grants PHY 1444389 , PHY 1505000 , CMMI 1125290 , and CHE-1213217 , and by DTRA Grant HDTRA1-14-1-0017 and DOE Contract DE-AC07-05Id14517 . This work was partially supported by Baltic-American Freedom Foundation and CIEE .

FundersFunder number
National Science FoundationPHY 1444389, PHY 1505000, HDTRA1-14-1-0017, CMMI 1125290, CHE-1213217
U.S. Department of EnergyDE-AC07-05Id14517
California Institute of Energy and Environment
Baltic-American Freedom Foundation


    • Agent-based modeling
    • Financial markets
    • Return intervals
    • Scaling behavior
    • Volatility


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