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Empirical Economics

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01.01.2006 | Original Paper

Liquidity supply and adverse selection in a pure limit order book market

verfasst von: Stefan Frey, Joachim Grammig

Erschienen in: Empirical Economics | Ausgabe 4/2006

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Abstract

This paper analyzes adverse selection costs and liquidity supply in a pure open limit order book market. We relax assumptions of the Glosten/Såndas modeling framework regarding marginal zero profit order book equilibrium and the parametric market order size distribution. We show that using average zero profit conditions considerably increases the empirical performance while a nonparametric specification for market order size combined with marginal zero profit conditions does not. A cross sectional analysis corroborates the finding that adverse selection costs are more severe for smaller capitalized stocks. We also find additional support for one of the central hypothesis put forth by the theory of limit order book markets, which states that liquidity supply and adverse selection costs are inversely related. Furthermore, adverse selection cost estimates based on our structural model and those obtained using popular model-free methods are strongly correlated. This indicates the robustness of the theory-based approach.

Vorheriger Artikel Order aggressiveness and order book dynamics

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In January 2002 the New York Stock Exchange (NYSE), known as a hybrid specialist market, adopted the key feature of electronic order book markets, namely the public display of all limit orders (NYSE open book program).

Traditionally, market microstructure theory focussed on quote driven markets with one or more market makers (see O’Hara, 1995 for an overview). Recent papers by Parlour (1998), Seppi (1997), Foucault (1999) and Foucault et al. (2003) have changed the focus to the analysis of price and liquidity processes in order book markets.

The Xetra technology was recently licensed to the Shanghai Stock Exchange, China’s largest stock exchange.

The Xetra trading system resembles in many features other important limit order book markets around the world like Euronext, the joint trading platform of the Amsterdam, Brussels, Lisbon and Paris stock exchanges, the Hong Kong stock exchange described in Ahn et al. (2001) and the Australian stock exchange, described in Cao et al. (2004).

A marketable limit order is a limit order with a limit price that makes it immediately executable against the current book. In our study, ‘real’ market orders (i.e. orders submitted without an upper or lower price limit) and marketable limit orders are treated alike. Henceforth, both real market orders and marketable limit orders are referred to as market orders.

For example, Bauwens and Giot (2001) describe how the Paris Bourse’s trading protocol converted the volume of a market order in excess of the depth at the best quote into a limit order at that price which enters the opposite side of the order book.

By choosing a five minutes lag we follow the previous literature, see e.g. SEC (2001).

Boehmer (2004) and SEC (2001) conduct exhaustive comparisons of transaction costs and adverse selection effects in US exchanges based on effective and realized spread analyses.

In an alternative specification we allowed for additional flexibility by allowing the expected buy and sell market order sizes to be different. However, the parameter estimates and diagnostics changed only marginally. We therefore decided to stick to the specification in Eq. (2) which is more appealing both from a methodological and theoretical point of view.

We are grateful to a referee for pointing this out.

It should be noted that the exponential assumption in DeJong et al.’s (1996) implementation of the Glosten model did not seem to be a restrictive assumption.

For notational brevity we omit the subscripts. Market order size m and fundamental price X are observed at time t, and the equation holds for any price tick p _+k,t with associated cumulative volume Q _+k,t, k=1,2....

Two stage and iterated GMM estimates are similar and therefore not reported to conserve space. To compute the parameter standard errors and the J-statistic we employ the Bartlett Kernel with bandwidth equal to ten lags when computing the spectral density matrix. We have tested various lags and the results are robust with respect to bandwidth choice.

We have also estimated a specification that combines the nonparametric approach towards trades sizes and average moment conditions, but the results (not reported) are not improved compared to the parametric version. In this version, the model is not rejected for 16 out of 30 stocks. The following analysis therefore focuses on the parametric specification using average moment conditions.

Huang and Stoll (1996) and DeJong et al. (1996) provide evidence for a negative correlation of realized spread and adverse selection costs.

The exercise is analogous for the bid side, but to conserve space, we focus on the sell side of the book.

The same result can be derived using the precise probabilities and a first-order Taylor approximation for the emerging exponential terms.

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Titel: Liquidity supply and adverse selection in a pure limit order book market
verfasst von: Stefan Frey
Joachim Grammig
Publikationsdatum: 01.01.2006
Verlag: Springer-Verlag
Erschienen in: Empirical Economics / Ausgabe 4/2006
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-005-0009-6

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