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A Stationary Kyle Setup: Microfounding propagator models

Author

Listed:
  • Michele Vodret
  • Iacopo Mastromatteo
  • Bence Tóth
  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. Our setup generalizes the well-known Kyle model, by dropping the assumption of a terminal time at which fundamental information is revealed so to describe a stationary market, while retaining agents' rationality and asymmetric information. We investigate the stationary equilibrium for arbitrary Gaussian noise trades and fundamental information, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay. Our model provides a testable relation between volatility of prices, magnitude of fluctuations in fundamentals and level of volume traded in the market.

Suggested Citation

  • Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2021. "A Stationary Kyle Setup: Microfounding propagator models," Post-Print hal-03016486, HAL.
    • Handle: RePEc:hal:journl:hal-03016486
    Note: View the original document on HAL open archive server: https://hal.science/hal-03016486
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    References listed on IDEAS

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    1. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    2. Armand Joulin & Augustin Lefevre & Daniel Grunberg & Jean-Philippe Bouchaud, 2008. "Stock price jumps: news and volume play a minor role," Papers 0803.1769, arXiv.org.
    3. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    4. Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
    5. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    6. Dan Bernhardt & P. Seiler & B. Taub, 2010. "Speculative dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 1-52, July.
    7. repec:pri:cepsud:91malkiel is not listed on IDEAS
    8. Jean-Philippe Bouchaud, 2008. "Economics need a scientific revolution," Papers 0810.5306, arXiv.org.
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    10. Eric Benhamou, 2018. "Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets," Papers 1811.11618, arXiv.org, revised Dec 2018.
    11. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    12. Bart Taub, 2019. "Economic and financial modeling techniques in the frequency domain," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 1-17, May.
    13. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    14. Tóth, Bence & Palit, Imon & Lillo, Fabrizio & Farmer, J. Doyne, 2015. "Why is equity order flow so persistent?," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 218-239.
    15. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    16. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    17. Lorenzo Dall’amico & Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "How does latent liquidity get revealed in the limit order book?," Post-Print hal-02323373, HAL.
    18. Lorenzo Dall’amico & Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "How does latent liquidity get revealed in the limit order book?," Post-Print hal-02283821, HAL.
    19. Çetin, Umut, 2018. "Financial equilibrium with asymmetric information and random horizon," LSE Research Online Documents on Economics 84495, London School of Economics and Political Science, LSE Library.
    20. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact," Papers 1602.02735, arXiv.org.
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    Citations

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    Cited by:

    1. Francesco Cordoni & Fabrizio Lillo, 2022. "Transient impact from the Nash equilibrium of a permanent market impact game," Papers 2205.00494, arXiv.org, revised Mar 2023.
    2. Michele Vodret & Iacopo Mastromatteo & Bence T'oth & Michael Benzaquen, 2021. "Do fundamentals shape the price response? A critical assessment of linear impact models," Papers 2112.04245, arXiv.org.
    3. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    4. Michele Vodret & Bence Tóth & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Do fundamentals shape the price response? A critical assessment of linear impact models," Post-Print hal-03797375, HAL.

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