parlour - Information Acquisition in a Limit Order Market...

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Information Acquisition in a Limit Order Market * Ronald L. Goettler Christine A. Parlour Uday Rajan § May 30, 2006 Abstract We numerically solve a model with endogenous information acquisition in a limit order market.. The asset has a common value; in addition, each trader has a private value for it. Traders randomly arrive at the market, after choosing whether to purchase information about the common value. They may either post prices or accept posted prices. If a trader’s order has not executed, he randomly reenters the market, and may change his previous order. The model is thus a dynamic stochastic game with asymmetric information. Agents with the lowest intrinsic benefit from trade have the highest value for information and also tend to supply liquidity. Agents’ incentives to acquire information and subsequent equilibrium trading behavior changes systematically with the underlying volatility of the asset. This has two asset pricing implications. First, in equilibrium, asymmetric information creates a “volatility multiplier” (prices are more volatile than the fundamental value of the asset) that is higher, the higher the fundamental volatility. This is due to a change in the composition of trader types in the market at any given time. Second, changes in the di ff erence between any transaction price and the fundamental value are negatively correlated with the fundamental returns. This correlation is more negative, the more volatile the asset. This is due to a change in trading strategies. We conclude that estimates of any factor model systematically underestimate the true coe ffi cient, and this e ff ect is more severe the higher the exposure. Keywords: limit order market, adverse selection, informational e ffi ciency. JEL Codes : G14, C63, C73, D82. * We have benefitted greatly from comments provided by Kerry Back, Ekkehart Boehmer, Bill Lovejoy, Ben Van Roy, and seminar participants at Aladdin (2004), CFS (Eltville), Michigan, Carnegie Mellon, Texas A&M, the 2004 Oxford Finance Summer Symposium, the 2005 Utah WFC, and the 2005 INFORMS conference. The current version of this paper is maintained at http://webuser.bus.umich.edu/urajan/research/inform.pdf. Tepper School of Business, Carnegie Mellon University. Tel: (412) 268-7058, E-mail: [email protected] Tepper School of Business, Carnegie Mellon University, and Haas School of Business, University of California, Berkeley. Tel: 510-643-9391, E-mail: [email protected] § Ross School of Business, University of Michigan, Ann Arbor. Tel: (734) 764-2310, E-mail: [email protected]
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1 Introduction Financial markets are inherently dynamic: traders choose when to trade. As a result, the set of potential traders in the market, and hence transaction prices, can vary across time. Explicitly modeling this is important because, in a dynamic market, the price of the asset at any instant is determined by the last transaction. More precisely, as there are two sides to any transaction, prices depend on the valuations of the most desperate buyer and seller
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