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Kyle's Model with Stochastic Liquidity

Author

Listed:
  • Ibrahim Ekren
  • Brad Mostowski
  • Gordan v{Z}itkovi'c

Abstract

We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our equilibrium allows us to study the impact of the stochastic volatility of noise trading on the volatility of the asset. In particular, when the fundamental price is log-normally distributed, informed trading forces the log-return up to maturity to be Gaussian for any choice of noise-trading volatility even though the price process itself comes with stochastic volatility. Surprisingly, we find that in equilibrium both Kyle's Lambda and its inverse (the market depth) are submartingales.

Suggested Citation

  • Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    • Handle: RePEc:arx:papers:2204.11069
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    References listed on IDEAS

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    1. Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
    2. Choi, Jin Hyuk & Larsen, Kasper & Seppi, Duane J., 2019. "Information and trading targets in a dynamic market equilibrium," Journal of Financial Economics, Elsevier, vol. 132(3), pages 22-49.
    3. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    4. Chao Ying, 2020. "The Pre-FOMC Announcement Drift and Private Information: Kyle Meets Macro-Finance," 2020 Papers pyi149, Job Market Papers.
    5. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2020. "The Multivariate Kyle model: More is different," Post-Print hal-02323433, HAL.
    6. Guillaume Lasserre, 2004. "Asymmetric information and imperfect competition in a continuous time multivariate security model," Finance and Stochastics, Springer, vol. 8(2), pages 285-309, May.
    7. Kerry Back & Kevin Crotty & Tao Li, 2018. "Identifying Information Asymmetry in Securities Markets," The Review of Financial Studies, Society for Financial Studies, vol. 31(6), pages 2277-2325.
    8. Pierre Collin‐Dufresne & Vyacheslav Fos, 2016. "Insider Trading, Stochastic Liquidity, and Equilibrium Prices," Econometrica, Econometric Society, vol. 84, pages 1441-1475, July.
    9. RenÈ Caldentey & Ennio Stacchetti, 2010. "Insider Trading With a Random Deadline," Econometrica, Econometric Society, vol. 78(1), pages 245-283, January.
    10. Pierre Collin‐Dufresne & Vyacheslav Fos, 2016. "Insider Trading, Stochastic Liquidity, and Equilibrium Prices," Econometrica, Econometric Society, vol. 84(4), pages 1441-1475, July.
    11. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    12. Baruch, Shmuel, 2002. "Insider trading and risk aversion," Journal of Financial Markets, Elsevier, vol. 5(4), pages 451-464, October.
    13. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
    14. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    15. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    16. Kerry Back & Francois Cocquemas & Ibrahim Ekren & Abraham Lioui, 2020. "Optimal Transport and Risk Aversion in Kyle's Model of Informed Trading," Papers 2006.09518, arXiv.org, revised Aug 2021.
    17. Caballe, Jordi & Krishnan, Murugappa, 1994. "Imperfect Competition in a Multi-security Market with Risk Neutrality," Econometrica, Econometric Society, vol. 62(3), pages 695-704, May.
    18. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    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. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    21. Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
    22. Campi, Luciano & Çetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 534-567, March.
    23. Weston Barger & Ryan Donnelly, 2021. "Insider Trading With Temporary Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-32, March.
    24. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    25. Collin-Dufresne, Pierre & Fos, Vyacheslav & Muravyev, Dmitry, 2021. "Informed Trading in the Stock Market and Option-Price Discovery," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 56(6), pages 1945-1984, September.
    26. Subrahmanyam, Avanidhar, 1991. "Risk Aversion, Market Liquidity, and Price Efficiency," The Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 416-441.
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