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Structural and topological phase transitions on the German Stock Exchange

Author

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  • Wiliński, M.
  • Sienkiewicz, A.
  • Gubiec, T.
  • Kutner, R.
  • Struzik, Z.R.

Abstract

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela–Chakraborti–Kaski–Kertész for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.

Suggested Citation

  • Wiliński, M. & Sienkiewicz, A. & Gubiec, T. & Kutner, R. & Struzik, Z.R., 2013. "Structural and topological phase transitions on the German Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5963-5973.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:23:p:5963-5973
    DOI: 10.1016/j.physa.2013.07.064
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    References listed on IDEAS

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    1. A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach," Papers 1301.6506, arXiv.org.
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    Cited by:

    1. Brida, Juan Gabriel & Matesanz, David & Seijas, Maria Nela, 2016. "Network analysis of returns and volume trading in stock markets: The Euro Stoxx case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 751-764.
    2. Nie, Chun-Xiao & Song, Fu-Tie & Li, Sai-Ping, 2016. "Rényi indices of financial minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 883-889.
    3. Coletti, Paolo, 2016. "Comparing minimum spanning trees of the Italian stock market using returns and volumes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 246-261.
    4. Matesanz, David & Ortega, Guillermo J., 2015. "Sovereign public debt crisis in Europe. A network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 756-766.
    5. repec:kap:compec:v:51:y:2018:i:2:d:10.1007_s10614-017-9672-x is not listed on IDEAS
    6. Nobi, Ashadun & Maeng, Seong Eun & Ha, Gyeong Gyun & Lee, Jae Woo, 2014. "Effects of global financial crisis on network structure in a local stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 135-143.

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