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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 392 (2013)
Issue (Month): 23 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R. Mantegna, 1999.
"Hierarchical structure in financial markets,"
The European Physical Journal B: Condensed Matter and Complex Systems,
Springer;EDP Sciences, 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;EDP Sciences, vol. 11(1), pages 193-197, September.
- 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.
- Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2000.
"High-frequency Cross-correlation in a Set of Stocks,"
cond-mat/0009350, arXiv.org, revised Nov 2000.
- G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
- 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;EDP Sciences, vol. 66(1), pages 91-96, November.
- 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.
- 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.
- 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.
- Didier SORNETTE, . "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
- 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.
- 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;EDP Sciences, 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;EDP Sciences, 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.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:392:y:2013:i:23:p:5963-5973. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.