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Return Intervals Approach to Financial Fluctuations

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Book cover Complex Sciences (Complex 2009)

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Abstract

Financial fluctuations play a key role for financial markets studies. A new approach focusing on properties of return intervals can help to get better understanding of the fluctuations. A return interval is defined as the time between two successive volatilities above a given threshold. We review recent studies and analyze the 1000 most traded stocks in the US stock markets. We find that the distribution of the return intervals has a well approximated scaling over a wide range of thresholds. The scaling is also valid for various time windows from one minute up to one trading day. Moreover, these results are universal for stocks of different countries, commodities, interest rates as well as currencies. Further analysis shows some systematic deviations from a scaling law, which are due to the nonlinear correlations in the volatility sequence. We also examine the memory in return intervals for different time scales, which are related to the long-term correlations in the volatility. Furthermore, we test two popular models, FIGARCH and fractional Brownian motion (fBm). Both models can catch the memory effect but only fBm shows a good scaling in the return interval distribution.

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Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA

    Fengzhong Wang, Kazuko Yamasaki, Shlomo Havlin & H. Eugene Stanley

  2. Department of Environmental Sciences, Tokyo University of Information Sciences, Chiba, 265-8501, Japan

    Kazuko Yamasaki

  3. Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Shlomo Havlin

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  1. Fengzhong Wang
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  1. Network Technology Research Centre, Research Techno Plaza, Nanyang Technology University, 4th story X‘Frontiers, Block 50 Nanyang Drive, 637553, Singapore

    Jie Zhou

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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

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Wang, F., Yamasaki, K., Havlin, S., Stanley, H.E. (2009). Return Intervals Approach to Financial Fluctuations. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-02466-5_1

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