IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v22y2018i1d10.1007_s00780-017-0348-0.html
   My bibliography  Save this article

Financial equilibrium with asymmetric information and random horizon

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-017-0348-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-017-0348-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. Çetin, Umut & Danilova, Albina, 2016. "Markov bridges: SDE representation," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 651-679.
    5. repec:dau:papers:123456789/4436 is not listed on IDEAS
    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. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    9. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    10. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    11. 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.
    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Umut c{C}etin, 2016. "Financial equilibrium with asymmetric information and random horizon," Papers 1603.08828, arXiv.org, revised Sep 2017.
    2. Umut c{C}et{i}n, 2018. "Mathematics of Market Microstructure under Asymmetric Information," Papers 1809.03885, arXiv.org.
    3. 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.
    4. José Manuel Corcuera & Giulia Di Nunno, 2018. "Kyle–Back’S Model With A Random Horizon," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-41, March.
    5. Dimitri Vayanos & Jiang Wang, 2012. "Market Liquidity -- Theory and Empirical Evidence," NBER Working Papers 18251, National Bureau of Economic Research, Inc.
    6. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.
    7. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    8. Luke M. Bennett & Wei Hu, 2023. "Filtration enlargement‐based time series forecast in view of insider trading," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 112-140, February.
    9. Umut c{C}etin & Hao Xing, 2012. "Point process bridges and weak convergence of insider trading models," Papers 1205.4358, arXiv.org, revised Jan 2013.
    10. Luciano Campi & Umut Cetin & Albina Danilova, 2011. "Equilibrium model with default and insider's dynamic information," Working Papers hal-00613216, HAL.
    11. 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.
    12. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    13. 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.
    14. 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.
    15. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh & Lu Vy, 2022. "A unified approach to informed trading via Monge-Kantorovich duality," Papers 2210.17384, arXiv.org.
    16. José Manuel Corcuera & Giulia Nunno & José Fajardo, 2019. "Kyle equilibrium under random price pressure," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 77-101, June.
    17. Jos'e Manuel Corcuera & Giulia Di Nunno & Gergely Farkas & Bernt {O}ksendal, 2014. "A continuous auction model with insiders and random time of information release," Papers 1411.2835, arXiv.org, revised Mar 2018.
    18. Sastry, Ravi & Thompson, Rex, 2019. "Strategic trading with risk aversion and information flow," Journal of Financial Markets, Elsevier, vol. 44(C), pages 1-16.
    19. Cetin, Umut & Xing, Hao, 2013. "Point process bridges and weak convergence of insider trading models," LSE Research Online Documents on Economics 48745, London School of Economics and Political Science, LSE Library.
    20. Luciano Campi & Umut Çetin & Albina Danilova, 2013. "Equilibrium model with default and dynamic insider information," Finance and Stochastics, Springer, vol. 17(3), pages 565-585, July.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0348-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.