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Price Dynamics on a Stock Market with Asymmetric Information

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  • Bernard De Meyer

Abstract

The appearance of a Brownian term in the price dynamics on a stock market was interpreted in [De Meyer, Moussa-Saley (2003)] as a consequence of the informational asymmetries between agents. To take benefit of their private information without revealing it to fast, the informed agents have to introduce a noise on their actions, and all these noises introduced in the day after day transactions for strategic reasons will aggregate in a Brownian Motion. We prove in the present paper that this kind of argument leads not only to the appearance of the Brownian motion, but it also narrows the class of the price dynamics: the price process will be, as defined in this paper, a continuous martingale of maximal variation. This class of dynamics contains in particular Black and Scholes' as well as Bachelier's dynamics. The main result in this paper is that this class is quite universal and independent of a particular model: the informed agent can choose the speed of revelation of his private information. He determines in this way the posterior martingale L, where L_{q} is the expected value of an asset at stage q given the information of the uninformed agents. The payoff of the informed agent at stage q can typically be expressed as a 1-homogeneous function M of L_{q+1}-L_{q}. In a game with n stages, the informed agent will therefore chose the martingale L? that maximizes the M-variation. Under a mere continuity hypothesis on M, we prove in this paper that L? will converge to a continuous martingale of maximal variation. This limit is independent of M.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000841.

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Date of creation: 07 Mar 2007
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Handle: RePEc:cla:levrem:321307000000000841

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  1. DE MEYER, Bernard, 1996. "The Maximal Variation of a Bounded Martingale and the Central Limit Theorem," CORE Discussion Papers 1996035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Documents de travail du Centre d'Economie de la Sorbonne 09035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  4. Bernard De Meyer & Alexandre Marino, 2005. "Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00193996, HAL.
  5. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. DE MEYER, Bernard & MOUSSA SALEY, Hadiza, 2000. "On the strategic origin of Brownian motion in finance," CORE Discussion Papers 2000057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer, vol. 36(2), pages 241-257, October.
  8. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Victor Domansky & Victoria Kreps, 2012. "Game-theoretic model of financial markets with two risky assets," HSE Working papers WP BRP 16/EC/2012, National Research University Higher School of Economics.
  2. Pierre Cardaliaguet & Catherine Rainer, 2012. "Games with Incomplete Information in Continuous Time and for Continuous Types," Dynamic Games and Applications, Springer, vol. 2(2), pages 206-227, June.
  3. Shino Takayama, 2013. "Price Manipulation, Dynamic Informed Trading and Tame Equilibria: Theory and Computation," Discussion Papers Series 492, School of Economics, University of Queensland, Australia.

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