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Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles

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  • Maximilian Seyrich

    (Department of Physics, ETH Zurich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland2Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany)

  • Didier Sornette

    (Chair of Entrepreneurial Risk, ETH Zurich, Scheuchzerstrasse 7, 8092 Zuerich, Switzerland4Swiss Finance Institute, c/o University of Geneva, 40 blvd. Du Pont d’Arve, CH 1211 Geneva 4, Switzerland)

Abstract

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen–Ledoit–Sornette (JLS) model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a>1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modeling the density of traders on the percolation network by an Ornstein–Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.

Suggested Citation

  • Maximilian Seyrich & Didier Sornette, 2016. "Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(10), pages 1-20, October.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:10:n:s0129183116501138
    DOI: 10.1142/S0129183116501138
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    Citations

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    Cited by:

    1. Zhang, Qunzhi & Sornette, Didier & Balcilar, Mehmet & Gupta, Rangan & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2016. "LPPLS bubble indicators over two centuries of the S&P 500 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 126-139.
    2. Samuel W. Akingbade & Marian Gidea & Matteo Manzi & Vahid Nateghi, 2023. "Why Topological Data Analysis Detects Financial Bubbles?," Papers 2304.06877, arXiv.org.
    3. Riza Demirer & Guilherme Demos & Rangan Gupta & Didier Sornette, 2019. "On the predictability of stock market bubbles: evidence from LPPLS confidence multi-scale indicators," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 843-858, May.

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