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Bubbles and crashes: Gradient dynamics in financial markets

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  • Friedman, Daniel
  • Abraham, Ralph

Abstract

Fund managers respond to the payoff gradient by continuously adjusting leverage in our analytic and simulation models. The base model has a stable equilibrium with classic properties. However, bubbles and crashes occur in extended models incorporating an endogenous market risk premium based on investors' historical losses and constant-gain learning. When losses have been small for a long time, asset prices inflate as fund managers increase leverage. Then slight losses can trigger a crash, as a widening risk premium accelerates deleveraging and asset price declines.

Suggested Citation

  • Friedman, Daniel & Abraham, Ralph, 2009. "Bubbles and crashes: Gradient dynamics in financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 922-937, April.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:4:p:922-937
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    3. Italo Bischi, Gian & Lamantia, Fabio, 2012. "A dynamic model of oligopoly with R&D externalities along networks. Part II," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 66-82.
    4. Breuer, Thomas & Jandačka, Martin & Summer, Martin & Vollbrecht, Hans-Joachim, 2015. "Endogenous leverage and asset pricing in double auctions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 144-160.
    5. Prajwal Eachempati & Praveen Ranjan Srivastava, 2021. "Accounting for unadjusted news sentiment for asset pricing," Qualitative Research in Financial Markets, Emerald Group Publishing Limited, vol. 13(3), pages 383-422, May.
    6. Gaffeo, Edoardo, 2019. "Leverage and evolving heterogeneous beliefs in a simple agent-based financial market," Finance Research Letters, Elsevier, vol. 29(C), pages 272-279.
    7. Xu, Hai-Chuan & Zhang, Wei & Xiong, Xiong & Wang, Xue & Zhou, Wei-Xing, 2021. "The double-edged role of social learning: Flash crash and lower total volatility," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 405-420.
    8. Feldman, Todd, 2011. "Leverage regulation: An agent-based simulation," Journal of Economics and Business, Elsevier, vol. 63(5), pages 431-440, September.
    9. Friedman, Daniel & Isaac, R. Mark & James, Duncan & Sunder, Shyam, 2014. "Risky Curves: On the Empirical Failure of Expected Utility," Santa Cruz Department of Economics, Working Paper Series qt87v8k86z, Department of Economics, UC Santa Cruz.
    10. Emmanuel Carré & Laurent Le Maux, 2024. "Bernanke and Kindleberger on financial crises, 1978–2003," Oxford Economic Papers, Oxford University Press, vol. 76(2), pages 314-329.
    11. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    12. Lai, Chong, 2022. "Investment dynamics of fund managers under evolutionary games," International Review of Financial Analysis, Elsevier, vol. 82(C).
    13. Feldman, Todd, 2018. "Unwinding ZIRP: A simulation analysis," Finance Research Letters, Elsevier, vol. 24(C), pages 278-288.
    14. V. I. Yukalov & E. P. Yukalova & D. Sornette, 2015. "Dynamical system theory of periodically collapsing bubbles," Papers 1507.05311, arXiv.org.
    15. Todd Feldman & Gabriele Lepori, 2016. "Asset price formation and behavioral biases," Review of Behavioral Finance, Emerald Group Publishing Limited, vol. 8(2), pages 137-155, November.
    16. Li, Minqiang, 2010. "A damped diffusion framework for financial modeling and closed-form maximum likelihood estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 132-157, February.

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