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Market Fragility, Systemic Risk, and Ricci Curvature

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  • Romeil Sandhu
  • Tryphon Georgiou
  • Allen Tannenbaum

Abstract

Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have shown that representing such systems as a weighted graph characterizing the complex web of interacting agents over some information flow (e.g., debt, stock returns, shareholder ownership) may provide certain keen insights. Here, we show that fragility, or the ability of system to be prone to failures in the face of random perturbations, is negatively correlated with geometric notion of Ricci curvature. The key ingredient relating fragility and curvature is entropy. As a proof of concept, we examine returns from a set of stocks comprising the S\&P 500 over a 15 year span to show that financial crashes are more robust compared to normal "business as usual" fragile market behavior - i.e., Ricci curvature is a "crash hallmark." Perhaps more importantly, this work lays the foundation of understanding of how to design systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007-2008 crisis.

Suggested Citation

  • Romeil Sandhu & Tryphon Georgiou & Allen Tannenbaum, 2015. "Market Fragility, Systemic Risk, and Ricci Curvature," Papers 1505.05182, arXiv.org.
  • Handle: RePEc:arx:papers:1505.05182
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    References listed on IDEAS

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    Cited by:

    1. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    2. Wanxiao Tang & Jun Zhao & Peibiao Zhao, 2019. "Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs," JRFM, MDPI, vol. 12(1), pages 1-17, February.

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