Security Bid/Ask Dynamics with Discreteness and Clustering: Simple Strategies for Modeling and Estimation

The short-term movements of a security price reflect the latent efficient price (conditional expectation of terminal value) and also components arising from the trading mechanism itself. Observed bid and ask quotes are but rough signals of these unobserved quantities. The bid and ask quotes in the $/DM market considered here, for example, are discrete, with a tick size that is not trivial relative to the spread. Furthermore, the distribution of these quotes is clustered, with a greater-than-expected incidence of five-tick multiples. This paper suggests a simple framework for handling discrete, clustered quotes. Despite the simplicity of the model, estimation by traditional (likelihood or moment) methods is difficult. As an alternative, the paper implements a Gibbs sampler approach that proves to be quick and effective. This strategy opens the door for the investigation of a broad class of structural microstructure models.

[1]  T. Fearn,et al.  Bayesian statistics : principles, models, and applications , 1990 .

[2]  Richard K. Lyons,et al.  Optimal Transparency in a Dealer Market with an Application to Foreign Exchange , 1996 .

[3]  Gary Gottlieb,et al.  Implications of the Discreteness of Observed Stock Prices , 1985 .

[4]  L. Harris.  Estimation of Stock Price Variances and Serial Covariances from Discrete Observations , 1990 .

[5]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[6]  L. Harris,et al.  A maximum likelihood approach for non-Gaussian stochastic volatility models , 1998 .

[7]  R. Lyons,et al.  Tests of Microstructural Hypotheses in the Foreign Exchange Market , 1993 .

[8]  Henry P. Wynn,et al.  Generalised confounding with Grobner bases , 1996 .

[9]  Hendrik Bessembinder,et al.  Bid-ask spreads in the interbank foreign exchange markets☆ , 1994 .

[10]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[11]  Aurora García.  Econometric analysis of limited dependent time series. , 1997 .

[12]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[13]  T. Schelling.  The Strategy of Conflict , 1963 .

[14]  P. Schultz,et al.  Market Structure and the Intraday Pattern of Bid-Ask Spreads for NASDAQ Securities , 1995 .

[15]  Prajit K. Dutta,et al.  Competition and Collusion in Dealer Markets , 1997 .

[16]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[17]  Tarun Chordia,et al.  Market Making, the Tick Size, and Payment-for-Order Flow: Theory and Evidence , 1995 .

[18]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[19]  L. Harris.  Minimum Price Variations, Discrete Bid-Ask Spreads, and Quotation Sizes , 1994 .

[20]  Jeffrey A. Frankel,et al.  The Microstructure of Foreign Exchange Markets , 1996 .

[21]  Joel Hasbrouck,et al.  Modeling Market Microstructure Time Series , 1996 .

[22]  N. Shephard.  Partial non-Gaussian state space , 1994 .

[23]  Neil Shephard,et al.  Simulation�?Based Likelihood Inference for Limited Dependent Processes , 1998 .

[24]  Tim Bollerslev,et al.  Bid—ask spreads and volatility in the foreign exchange market: An empirical analysis , 1994 .

[25]  A. Kalay,et al.  Market Making with Discrete Prices , 1998 .

[26]  W. Torous,et al.  The degree of price resolution: The case of the gold market , 1985 .

[27]  L. Harris.  Stock Price Clustering and Discreteness , 1991 .

[28]  Michael K. Pitt,et al.  Likelihood Analysis of Non-Gaussian Parameter-Driven Models , 1995 .

[29]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[30]  A. Lo,et al.  An Ordered Probit Analysis of Transaction Stock Prices , 1991 .

[31]  C. Cao,et al.  Tick Size, Spread, and Volume , 1996 .

[32]  L. Lau,et al.  The sources of Asian Pacific economic growth , 1996 .

[33]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[34]  C. Ball,et al.  Estimation Bias Induced by Discrete Security Prices , 1988 .

[35]  Maureen O'Hara,et al.  Market Microstructure Theory , 1995 .

[36]  G. Kitagawa.  Non-Gaussian State—Space Modeling of Nonstationary Time Series , 1987 .

[37]  One Day in June, 1994: A Study of the Working of Reuters 2000-2 Electronic Foreign Exchange Trading System , 1995 .

[38]  James Angel.  Tick Size, Share Prices, and Stock Splits , 1997 .

[39]  D. Bernhardt,et al.  Discrete Pricing and the Design of Dealership Markets , 1996 .

[40]  L. Glosten.  Is the Electronic Open Limit Order Book Inevitable , 1994 .

[41]  Lawrence Harris,et al.  Estimating the components of the bid/ask spread , 1988 .

[42]  Bettina Peiers,et al.  Informed Traders, Intervention and Price Leadership: A Deeper View of the Microstructure of the Foreign Exchange Market , 1997 .

[43]  P. Schultz,et al.  Why Do NASDAQ Market Makers Avoid Odd-Eighth Quotes? , 1994 .

[44]  Thierry Foucault,et al.  Minimum Price Variations, Time Priority and Quote Dynamics , 1999 .

[45]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[46]  Eugene Kandel,et al.  NASDAQ Market Structure and Spread Patterns , 1997 .

[47]  P. Schultz,et al.  Why Did NASDAQ Market Makers Stop Avoiding Odd‐Eighth Quotes? , 1994 .

[48]  Andrew L. Rukhin,et al.  Tools for statistical inference , 1991 .

[49]  L. Harris.  Decimalization: A Review of the Arguments and Evidence , 1997 .

[50]  P. D. Jong.  The Diffuse Kalman Filter , 1991 .

[51]  Joel Hasbrouck,et al.  The Dynamics of Discrete Bid and Ask Quotes , 1996 .

[52]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[53]  N. Shephard,et al.  The simulation smoother for time series models , 1995 .

[54]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[55]  G. William Schwert.  Symposium on market microstructure: Focus on Nasdaq , 1997 .

[56]  Siddhartha Chib,et al.  Markov Chain Monte Carlo Simulation Methods in Econometrics , 1996, Econometric Theory.

[57]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[58]  David J. Spiegelhalter,et al.  Introducing Markov chain Monte Carlo , 1995 .