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Financial equilibrium with asymmetric information and random horizon

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  • Umut c{C}etin

Abstract

We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, 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 \cite{BB}. 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 $0$.

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  • Umut c{C}etin, 2016. "Financial equilibrium with asymmetric information and random horizon," Papers 1603.08828, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1603.08828
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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. Çetin, Umut & Danilova, Albina, 2016. "Markov bridges: SDE representation," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 651-679.
    4. 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.
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    6. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    7. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    8. repec:dau:papers:123456789/4436 is not listed on IDEAS
    9. 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.
    10. 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.
    11. 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.
    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.
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