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Financial equilibrium with asymmetric information and random horizon

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  • Çetin, Umut

Abstract

We study in detail and explicitly solve the version of Kyle’s model introduced in a specific case in [2], where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensional diffusions. It turns out that such an equilibrium is only possible if the final payoff is Bernoulli distributed as in [2]. We show in the second part that the signal of the market makers use in the general case is a time-changed version of the one that they would have used had the final payoff had a Bernoulli distribution. In both cases we characterise explicitly the equilibrium price process and the optimal strategy of the informed trader. Contrary to the original Kyle model it is found that the reciprocal of market’s depth, i.e. Kyle’s lambda, is a uniformly integrable supermartingale. While Kyle’s lambda is a potential, i.e. converges to 0, for the Bernoulli distributed final payoff, its limit in general is different than 0.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:84495
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    File URL: http://eprints.lse.ac.uk/84495/
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    References listed on IDEAS

    as
    1. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    3. repec:dau:papers:123456789/4436 is not listed on IDEAS
    4. 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.
    5. Pierre Collin-Dufresne & Vyacheslav Fos & Dmitriy Muravyev, 2015. "Informed Trading and Option Prices: Evidence from Activist Trading," Swiss Finance Institute Research Paper Series 15-55, Swiss Finance Institute, revised Nov 2015.
    6. Kerry Back & C. Henry Cao & Gregory A. Willard, 2000. "Imperfect Competition among Informed Traders," Journal of Finance, American Finance Association, vol. 55(5), pages 2117-2155, October.
    7. Campi, Luciano & Cetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," LSE Research Online Documents on Economics 31538, London School of Economics and Political Science, LSE Library.
    8. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    9. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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    Citations

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    Cited by:

    1. Michele Vodret & Iacopo Mastromatteo & Bence T'oth & Michael Benzaquen, 2020. "A Stationary Kyle Setup: Microfounding propagator models," Papers 2011.10242, arXiv.org, revised Feb 2021.
    2. Christoph Kuhn & Christopher Lorenz, 2023. "Insider trading in discrete time Kyle games," Papers 2312.00904, arXiv.org, revised Jul 2024.
    3. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2020. "A Stationary Kyle Setup: Microfounding propagator models," Working Papers hal-03016486, HAL.
    4. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2021. "A Stationary Kyle Setup: Microfounding propagator models," Post-Print hal-03016486, HAL.
    5. Luca Galimberti & Anastasis Kratsios & Giulia Livieri, 2022. "Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis," Papers 2210.13300, arXiv.org, revised May 2023.
    6. Cetin, Umut & Danilova, Albina, 2021. "On pricing rules and optimal strategies in general Kyle-Back models," LSE Research Online Documents on Economics 113003, London School of Economics and Political Science, LSE Library.
    7. Jin Hyuk Choi & Heeyoung Kwon & Kasper Larsen, 2022. "Trading constraints in continuous-time Kyle models," Papers 2206.08117, arXiv.org.
    8. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    9. Peter Bank & Yan Dolinsky & Mikl'os R'asonyi, 2021. "What if we knew what the future brings? Optimal investment for a frontrunner with price impact," Papers 2108.04291, arXiv.org, revised May 2022.
    10. Umut c{C}etin, 2023. "Insider trading with penalties, entropy and quadratic BSDEs," Papers 2311.12743, arXiv.org.
    11. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    12. Umut c{C}etin & Albina Danilova, 2018. "On pricing rules and optimal strategies in general Kyle-Back models," Papers 1812.07529, arXiv.org, revised Aug 2021.

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    More about this item

    Keywords

    Kyle's model; financial equilibrium; one-dimensional diffusion; h-transform; potential theory;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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