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Financial equilibrium with asymmetric information and random horizon

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  • Umut Çetin

    (London School of Economics and Political Science)

Abstract

We study in detail and explicitly solve the version of Kyle’s model introduced in a specific case in Back and Baruch (Econometrica 72:433–465, 2004), 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 Back and Baruch (Econometrica 72:433–465, 2004). We show in the second part that the signal the market makers use in the general case is a time-changed version of the one 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. In contrast to the original Kyle model, it is found that the reciprocal of the 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 from 0.

Suggested Citation

  • Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0348-0
    DOI: 10.1007/s00780-017-0348-0
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    References listed on IDEAS

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    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. Çetin, Umut & Danilova, Albina, 2016. "Markov bridges: SDE representation," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 651-679.
    7. 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.
    8. 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.
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    10. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    11. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    12. Foster, F Douglas & Viswanathan, S, 1996. "Strategic Trading When Agents Forecast the Forecasts of Others," Journal of Finance, American Finance Association, vol. 51(4), pages 1437-1478, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    2. Christoph Kuhn & Christopher Lorenz, 2023. "Insider trading in discrete time Kyle games," Papers 2312.00904, arXiv.org.
    3. 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.
    4. 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.
    5. Umut c{C}etin, 2023. "Insider trading with penalties, entropy and quadratic BSDEs," Papers 2311.12743, arXiv.org.
    6. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    7. 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.
    8. 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.
    9. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2020. "A Stationary Kyle Setup: Microfounding propagator models," Working Papers hal-03016486, HAL.
    10. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2021. "A Stationary Kyle Setup: Microfounding propagator models," Post-Print hal-03016486, HAL.
    11. Jin Hyuk Choi & Heeyoung Kwon & Kasper Larsen, 2022. "Trading constraints in continuous-time Kyle models," Papers 2206.08117, arXiv.org.
    12. 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.

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    More about this item

    Keywords

    Kyle’s model; Financial equilibrium; One-dimensional diffusions; h $h$ -transform; Potential theory;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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