Price Jump Prediction in a Limit Order Book

Affiliation(s)

Natixis, Equity Markets, Paris, France; Departement TSI, Télécom ParisTech, Paris, France; BNP Paribas Chair of Quantitative Finance, Ecole Centrale Paris, MAS Laboratory, Chatenay-Malabry, France.

Departement TSI, Télécom ParisTech, Paris, France.

Natixis, Equity Markets, Paris, France; Departement TSI, Télécom ParisTech, Paris, France; BNP Paribas Chair of Quantitative Finance, Ecole Centrale Paris, MAS Laboratory, Chatenay-Malabry, France.

Departement TSI, Télécom ParisTech, Paris, France.

ABSTRACT

A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that the liquidity balance on the best bid/best ask is quite informative for predicting the future market order’s direction. Moreover, we define price jump as a sell (buy) market order arrival which is executed at a price which is smaller (larger) than the best bid (best ask) price at the moment just after the precedent market order arrival. Features are then extracted related to limit order volumes, limit order price gaps, market order information and limit order event information. Logistic regression is applied to predict the price jump from the features of a limit order book. LASSO logistic regression is introduced to help us make variable selection from which we are capable to highlight the importance of different features in predicting the future price jump. In order to get rid of the intraday data seasonality, the analysis is based on two separated datasets: morning dataset and afternoon dataset. Based on an analysis on forty largest French stocks of CAC40, we find that trade sign and market order size as well as the liquidity on the best bid (best ask) are consistently informative for predicting the incoming price jump.

KEYWORDS

Limit Order Book; High Frequency Trading; Price Jump; Trade-Through; Logistic Regression; LASSO

Limit Order Book; High Frequency Trading; Price Jump; Trade-Through; Logistic Regression; LASSO

Cite this paper

B. Zheng, E. Moulines and F. Abergel, "Price Jump Prediction in a Limit Order Book,"*Journal of Mathematical Finance*, Vol. 3 No. 2, 2013, pp. 242-255. doi: 10.4236/jmf.2013.32024.

B. Zheng, E. Moulines and F. Abergel, "Price Jump Prediction in a Limit Order Book,"

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[1] O. E. Barndor-Nielsen and N. Shephard, “Econometric of Testing for Jumps in Nancial Economics Using Bipower Variation,” Oxford Financial Research Centre, 2004.

[2] Y. At-Sahalia and J. Jacod, “Estimating the Degree of Activity of Jumps in High Frequency Data,” The Annals of Statistics, Vol. 37, No. 5A, 2009, pp. 2202-2244.

[3] A. Chakrabortia, I. Muni Toke, M. Patriarca and F. Abergel, “Econophysics: Empirical Facts and Agent-Based Models,” Elsevier, 2009.

[4] R. Cont, S. Stoikov and R. Talreja, “A Stochastic Model for Order Book Dynamics,” Operations Research, Vol. 58, 2010, pp. 549-563.

[5] F. Abergel, B. K. Chakrabarti, A. Chakraborti and M. Mitra, “Econophysics of Order Driven Markets,” In: Proceedings of the 5th Kolkata Econophysic Conference, New Economic Windows, Springer, 2011.

[6] R. Cont and A. De Larrard, “Price Dynamics in a Markovian Limit Order Book Market,” Social Science Research Network Working Paper Series, 2011.

[7] J. Hasbrouck, “Measuring the Information Content of Stock Trades,” Journal of Finance, Vol. 46, 1991, pp. 179-207.

[8] J. A. Hausman, A. W. Lo and A. C. MacKinlay, “An Ordered Probit Analysis of Transaction Stock Prices,” Journal of Financial Economics, Vol. 31, No. 3, 1992, pp. 319-379.

[9] D.B. Keim and A. Madhaven, “The Upstairs Market for Large-Block Transactions: Analysis and Measurement of Price Effects,” Review of Financial Studies, Vol. 9, No. 1, 1996, pp. 1-36.

[10] A. W. Lo, A. Craig MacKinlay and J. Zhang, “Econometric Models of Limit-Order Executions,” Journal of Financial Economics, Vol. 65, No. 1, 2002, pp. 31-71.

[11] F. Lillo, J. Doyne Farmer and R. N. Mantegna, “Master Curve for Price Impact Function,” Nature, Vol. 421, No. 6919, 2003, pp. 129-130.

[12] J. Hasbrouck, “Empirical Market Microstructure: The Institutions, Economics and Econometrics of Securities Trading,” 2006.

[13] C. Parlour and D. Seppi, “Limit Order Markets: A Survey”.

[14] E. Jondeau, A. Perilla and M. Rockinger, “Optimal Liquidation Strategies in Illiquid Markets,” Swiss Finance Institute Research Paper No. 09-24, 2008.

[15] J. Linnainmaa and I. Rosu, “Weather and Time Series Determinants of Liquidity in a Limit Order Market,” 2009.

[16] T. Foucault and A. J. Menkveld. Competition for Order Flow and Smart Order Routing Systems,” Journal of Finance, Vol. 63, No. 1, 2008, pp. 119-158. doi:10.1111/j.1540-6261.2008.01312.x

[17] F. Pomponio and F. Abergel, “Trade-Throughs: Empirical Facts. Application to Lead-Lag Measures,” Proceedings of the 5th Kolkata Econophysic Conference, Vol. 1, No. 1, 2011, pp. 3-6.

[18] A. Blazejewski and R. Coggins, “A Local Non-Parametric Model for Trade Sign Inference,” Physica A: Statistical Mechanics and Its Applications, Vol. 348, No. 1, 2005, pp. 481-495.

[19] T. Fletcher, Z. Hussain and J. Shawe-Taylor, “Multiple Kernel Learning on the Limit Order Book,” Quantitative Finance, 2010.

[20] M. Potters and J. P. Bouchaud, “More Statistical Properties of Order Books and Price Impact,” Physica A, Vol. 324, No. 1-2, 2003, pp. 133-140.

[21] D. C. Porter, “The Probability of a Trade at the Ask: An Examination of Interday and Intraday Behavior,” Journal of Financial and Quantitative Analysis, Vol. 27, No. 2, 1992, pp. 209-227.

[22] M. Aitken, A. Kua, P. Brown, T. Watter and H. Y. Izan, “An Intraday Analysis of the Probability of Trading on the Asx at the Asking Price,” Australian Journal of Management, Vol. 20, No. 2, 1995, pp. 115-154.

[23] R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, Vol. 58, No. 1, 1994, pp. 267-288.

[24] T. Hastie, R. Tibshirani and J. H. Friedman, “The Elements of Statistical Learning,” Springer, 2003.

[25] J. Claerbout and F. Muir, “Robust Modeling with Erratic Data,” Geophysics, Vol. 38, No. 5, 1973, pp. 826-844.

[26] H. L. Taylor, S. C. Banks and J. F. McCoy, “Deconvolution with the l 1 Norm,” Geophysics, Vol. 44, No. 1, 1979, pp. 39-52.

[27] F. Santosa and W. W. Symes, “Linear Inversion of Band-Limited Reection Seismograms,” SIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 4, 1986, pp. 1307-1330.

[28] S. S. Chen, D. L. Donoho and M. A. Saunders, “Atomic Decomposition by Basis Pursuit,” SIAM Journal on Scientific Computing, Vol. 20, No. 1, 1998, pp. 33-61.

[29] J. F. Germain and F. Roue, “Weak Convergence of the Regularization Path in Penalized M-Estimation,” Scandinavian Journal of Statistics, Vol. 37, No. 3, 2010, pp. 477-495.

[30] J. H. Friedman, T. Hastie and R. Tibshirani, “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, Vol. 33, No. 1, 2010, pp. 1-22.

[31] J. P. Bouchaud, J. D. Farmer and F. Lillo, “How Markets Slowly Digest Changes in Supply and Demand,” 2008.