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Stefan Frey . Joachim Grammig<br />

Liquidity supply and adverse selection<br />

<strong>in</strong> a pure limit order book market<br />

Abstract This paper analyzes adverse selection costs and liquidity supply <strong>in</strong> a<br />

pure open limit order book market. We relax assumptions <strong>of</strong> the Glosten/Såndas<br />

model<strong>in</strong>g framework regard<strong>in</strong>g marg<strong>in</strong>al zero pr<strong>of</strong>it order book equilibrium and the<br />

parametric market order size distribution. We show that us<strong>in</strong>g average zero pr<strong>of</strong>it<br />

conditions considerably <strong>in</strong>creases the empirical performance while a nonparametric<br />

specification for market order size comb<strong>in</strong>ed with marg<strong>in</strong>al zero pr<strong>of</strong>it conditions<br />

does not. A cross sectional analysis corroborates the f<strong>in</strong>d<strong>in</strong>g that adverse<br />

selection costs are more severe for smaller capitalized stocks. We also f<strong>in</strong>d<br />

additional support for one <strong>of</strong> the central hypothesis put forth by the theory <strong>of</strong> limit<br />

order book markets, which states that liquidity supply and adverse selection costs<br />

are <strong>in</strong>versely related. Furthermore, adverse selection cost estimates based on our<br />

structural model and those obta<strong>in</strong>ed us<strong>in</strong>g popular model-free methods are strongly<br />

correlated. This <strong>in</strong>dicates the robustness <strong>of</strong> the theory-based approach.<br />

Keywords Limit order book market . Liquidity supply . Adverse selection<br />

JEL Classification G10 . C32<br />

Stefan Frey is also doctoral student at the Graduiertenkolleg “Unternehmensentwicklung,<br />

Marktprozesse und Regulierung <strong>in</strong> dynamischen Entscheidungsmodellen”. Joachim Grammig is<br />

also research fellow at the Centre for F<strong>in</strong>ancial Research (CFR), Cologne. Earlier drafts <strong>of</strong> the<br />

paper were presented at the German F<strong>in</strong>ance Association’s 2004 annual meet<strong>in</strong>g, and sem<strong>in</strong>ars at<br />

the Universities Cologne, Konstanz, Mannheim and Tüb<strong>in</strong>gen, and the 2005 meet<strong>in</strong>g <strong>of</strong> the<br />

Vere<strong>in</strong> fuer Socialpolitik Econometrics Section as well as the 2005 MicF<strong>in</strong> Workshop <strong>in</strong> Madrid.<br />

S. Frey (*) . J. Grammig<br />

Faculty <strong>of</strong> Economics, Department <strong>of</strong> Statistics, Econometrics and Empirical Economics,<br />

University <strong>of</strong> Tüb<strong>in</strong>gen, Mohlstr. 36, 72074 Tüb<strong>in</strong>gen, Germany<br />

E-mail: stefan.frey@uni-tueb<strong>in</strong>gen.de<br />

E-mail: joachim.grammig@uni-tueb<strong>in</strong>gen.de

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