Structural and topological phase transitions on the German Stock Exchange
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.
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Volume (Year): 392 (2013)
Issue (Month): 23 ()
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- L. Kullmann & J. Kertesz & K. Kaski, 2002. "Time dependent cross correlations between different stock returns: A directed network of influence," Papers cond-mat/0203256, arXiv.org, revised May 2002.
- R. Mantegna, 1999.
"Hierarchical structure in financial markets,"
The European Physical Journal B - Condensed Matter and Complex Systems,
Springer, vol. 11(1), pages 193-197, September.
- R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 11(1), pages 193-197, September.
- Didier SORNETTE, . "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
- 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.
- F. Pozzi & T. Di Matteo & T. Aste, 2008. "Centrality And Peripherality In Filtered Graphs From Dynamical Financial Correlations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 927-950.
- Dong-Ming Song & Michele Tumminello & Wei-Xing Zhou & Rosario N. Mantegna, 2011. "Evolution of worldwide stock markets, correlation structure and correlation based graphs," Papers 1103.5555, arXiv.org.
- A. Z. Górski & S. Drożdż & J. Kwapień, 2008. "Scale free effects in world currency exchange network," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 66(1), pages 91-96, November.
- M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2006.
"Correlation based networks of equity returns sampled at different time horizons,"
physics/0605251, arXiv.org, revised Apr 2007.
- M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2007. "Correlation based networks of equity returns sampled at different time horizons," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 209-217, 01.
- B. M. Tabak & T. R. Serra & D. O. Cajueiro, 2010. "Topological properties of commodities networks," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 74(2), pages 243-249, March.
- S. Drozdz & J. Kwapien & J. Speth, 2010. "Coherent Patterns in Nuclei and in Financial Markets," Papers 1009.1105, arXiv.org.
- N. Vandewalle & F. Brisbois & X. Tordoir, 2001. "Non-random topology of stock markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 372-374, March.
- G. Bonanno & F. Lillo & R. N. Mantegna, 2001.
"High-frequency cross-correlation in a set of stocks,"
Taylor & Francis Journals, vol. 1(1), pages 96-104.
- Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2000. "High-frequency Cross-correlation in a Set of Stocks," Papers cond-mat/0009350, arXiv.org, revised Nov 2000.
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