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The bounds of heavy-tailed return distributions in evolving complex networks

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  • Jo~ao P. da Cruz
  • Pedro G. Lind

Abstract

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy-tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk.

Suggested Citation

  • Jo~ao P. da Cruz & Pedro G. Lind, 2011. "The bounds of heavy-tailed return distributions in evolving complex networks," Papers 1109.2803, arXiv.org, revised Jan 2013.
    • Handle: RePEc:arx:papers:1109.2803
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    References listed on IDEAS

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    2. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, September.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Neil Johnson & Thomas Lux, 2011. "Ecology and economics," Nature, Nature, vol. 469(7330), pages 302-303, January.
    5. Andrew G. Haldane & Robert M. May, 2011. "Systemic risk in banking ecosystems," Nature, Nature, vol. 469(7330), pages 351-355, January.
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    Cited by:

    1. Natalia Markovich, 2024. "Extremal properties of evolving networks: local dependence and heavy tails," Annals of Operations Research, Springer, vol. 339(3), pages 1839-1870, August.
    2. Natalia Markovich & Marijus Vaičiulis, 2023. "Extreme Value Statistics for Evolving Random Networks," Mathematics, MDPI, vol. 11(9), pages 1-35, May.
    3. Sandip Dutta & Vignesh Prabhu, 2019. "Effect of Franchised Business models on Fast Food Company Stock Prices in Recession and Recovery with Weibull Analysis," Papers 1912.12940, arXiv.org.
    4. Lee, Byung Kwon & Zhou, Rong & de Souza, Robert & Park, Jaehun, 2016. "Data-driven risk measurement of firm-to-firm relationships in a supply chain," International Journal of Production Economics, Elsevier, vol. 180(C), pages 148-157.

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