Price Dynamics on a Stock Market with Asymmetric Information

Bernard De Meyer

No 1604, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Asymmetric information; Price dynamics; Martingales of maximal variation; Repeated games (search for similar items in EconPapers)
JEL-codes: C72 C73 D44 G14 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2007-02
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published in Games and Economic Behavior (May 2010), 69(1): 42-71

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