Kazakh Mathematical Journal. 2020; : 44-53
Использование полной книги предельных заказов для прогнозирования скачка цен
Аннотация
Институциональные инвесторы, особенно высокочастотные трейдеры, используют информацию о заказах, содержащуюся в Книге Лимитных Заказов (LOB). Основная цель статьи - изучить, как полная информация о LOB может помочь в прогнозировании различных событий, представляющих интерес для инвесторов. Обычно LOB содержит общие объемы заказов по сотням цен. Использование полной информации наталкивается на проклятие размерности, которое проявляется в мультиколлинеарности, низкой значимости коэффициентов, завышенных дисперсиях оценки и большом времени вычислений. Из-за этих проблем объемы заказов по ценам, далеким от цен bid и ask, обычно не используются в процедурах прогнозирования. По этой причине мы называем такую информацию молчаливой толпой. Здесь мы предлагаем сводную меру молчаливой толпы и количественно оцениваем ее влияние на прогнозирование торгового скачка. Мы используем реалистично смоделированную LOB в качестве средства для экспериментов и логистическую регрессию в качестве инструмента прогнозирования. Полный код в Matlab включает 18 блоков.
Список литературы
1. Parlour C., Seppi D.J. Limit Order Market: A Survey, Elsevier: North-Holland, 2008.
2. Cont R. Statistical modeling of high-frequency financial data, Signal Processing Magazine, IEEE, 28 (2011), 16-25. https://doi.org/10.1109/msp.2011.941548.
3. Cont R., Stoikov S., Talreja R. A stochastic model for order book dynamics, Operations Research, 58 (2010), 549-563. https://doi.org/10.2139/ssrn.1273160.
4. He H., Kercheval A.N. A generalized birth-death stochastic model for high frequency order book dynamics, Quantitative Finance, 12 (2012), 547-557. https://doi.org/10.1080/14697688.2012.664926.
5. Rosu I. A dynamic model of the limit order book, Review of Financial Studies, 22 (2009), 4601-4641. https://doi.org/10.1093/rfs/hhp011.
6. Shek H.H.S. Modeling High Frequency Market Order Dynamics Using Self-Excited Point Process, SSRN, (2011), 1-22. http://dx.doi.org/10.2139/ssrn.1668160.
7. Bouchaud J.-P., Mezard M., Potters M. Statistical properties of stock order books: Empirical results and models, Quantitative Finance, 2 (2002), 251-256. https://doi.org/10.2139/ssrn.507362.
8. Foucault T., Kadan O., Kandel E. Limit order book as a market for liquidity, Review of Financial Studies, 18 (2005), 1171-1217. https://doi.org/10.1093/rfs/hhi029.
9. Jondeau E., Perilla A., Rockinger G. Optimal Liquidation Strategies in Illiquid Markets, Springer: Berlin Heidelberg, 553 (2005). https://doi.org/10.2139/ssrn.1431869.
10. Linnainmaa J.T., Rosu I. Weather and Time Series Determinants of Liquidity in a Limit Order Market, AFA 2009 San Francisco Meetings Paper. http://dx.doi.org/10.2139/ssrn.1108862.
11. Crammer K., Singer Y. On the algorithmic implementation of multiclass kernel-based vector machines, Journal of Machine Learning Research, 2 (2001), 265-292.
12. Tino P., Nikolaev N., Yao X. Volatility forecasting with sparse bayesian kernel models, In 4th International Conference on Computational Intelligence in Economics and Finance, 2005, 1052-1058.
13. Blazejewski A., Coggins R. A Local Non-Parametric Model for Trade Sign Inference, Physica A: Statistical Mechanics and Its Applications, 348 (2005), 481-495. https://doi.org/10.1016/j.physa.2004.09.033.
14. Zheng B., Moulines E., Abergel F. Price Jump Prediction in a Limit Order Book, Journal of Mathematical Finance, 3:2 (2013), 242-255. https://doi.org/10.4236/jmf.2013.32024.
15. Fletcher T., Shawe-Taylor J. Multiple Kernel Learning with Fisher Kernels for High Frequency Currency Prediction, Comput. Econ., 42 (2013), 217–240. https://doi.org/10.1007/s10614-012-9317-z.
16. Kercheval A.N., Zhang Y. Modelling high-frequency limit order book dynamics with support vector machines, Quantitative Finance, 15 (2015), 1315-1329. https://doi.org/10.1080/14697688.2015.1032546.
17. Platania F., Serrano P., Tapia M. Modelling the shape of the limit order book, Quantitative Finance, 18 (2018), 1575-1597. https://doi.org/10.1080/14697688.2018.1433312.
18. Brogaard J., Hendershott T., Riordan R. Price Discovery without Trading: Evidence from Limit Orders, The Journal of Finance, 74 (2019), 1621-1658. https://doi.org/10.1111/jofi.12769.
Kazakh Mathematical Journal. 2020; : 44-53
Using full limit order book for price jump prediction
Abstract
Institutional investors, especially high frequency traders, employ the order information contained in the Limit Order Book (LOB). The main purpose of the paper is to investigate how full information about the LOB can help in predicting the price jump. Normally, a full LOB contains total volumes of orders for hundreds of prices. Using the full information runs into the curse of dimensionality which manifests itself in multicollinearity, insignificant coefficients, inflated estimate variances and high computation time. Due to these problems, order volumes for prices that are distant from ask and bid prices are usually not used in prediction procedures. For this reason we call such information a silent crowd. Here we propose a summary measure of the silent crowd and quantify its influence on trade jump prediction. We use a realistically simulated LOB as a vehicle for experiments and logistic regression as the prediction tool. The full code in Matlab includes 18 blocks.
References
1. Parlour C., Seppi D.J. Limit Order Market: A Survey, Elsevier: North-Holland, 2008.
2. Cont R. Statistical modeling of high-frequency financial data, Signal Processing Magazine, IEEE, 28 (2011), 16-25. https://doi.org/10.1109/msp.2011.941548.
3. Cont R., Stoikov S., Talreja R. A stochastic model for order book dynamics, Operations Research, 58 (2010), 549-563. https://doi.org/10.2139/ssrn.1273160.
4. He H., Kercheval A.N. A generalized birth-death stochastic model for high frequency order book dynamics, Quantitative Finance, 12 (2012), 547-557. https://doi.org/10.1080/14697688.2012.664926.
5. Rosu I. A dynamic model of the limit order book, Review of Financial Studies, 22 (2009), 4601-4641. https://doi.org/10.1093/rfs/hhp011.
6. Shek H.H.S. Modeling High Frequency Market Order Dynamics Using Self-Excited Point Process, SSRN, (2011), 1-22. http://dx.doi.org/10.2139/ssrn.1668160.
7. Bouchaud J.-P., Mezard M., Potters M. Statistical properties of stock order books: Empirical results and models, Quantitative Finance, 2 (2002), 251-256. https://doi.org/10.2139/ssrn.507362.
8. Foucault T., Kadan O., Kandel E. Limit order book as a market for liquidity, Review of Financial Studies, 18 (2005), 1171-1217. https://doi.org/10.1093/rfs/hhi029.
9. Jondeau E., Perilla A., Rockinger G. Optimal Liquidation Strategies in Illiquid Markets, Springer: Berlin Heidelberg, 553 (2005). https://doi.org/10.2139/ssrn.1431869.
10. Linnainmaa J.T., Rosu I. Weather and Time Series Determinants of Liquidity in a Limit Order Market, AFA 2009 San Francisco Meetings Paper. http://dx.doi.org/10.2139/ssrn.1108862.
11. Crammer K., Singer Y. On the algorithmic implementation of multiclass kernel-based vector machines, Journal of Machine Learning Research, 2 (2001), 265-292.
12. Tino P., Nikolaev N., Yao X. Volatility forecasting with sparse bayesian kernel models, In 4th International Conference on Computational Intelligence in Economics and Finance, 2005, 1052-1058.
13. Blazejewski A., Coggins R. A Local Non-Parametric Model for Trade Sign Inference, Physica A: Statistical Mechanics and Its Applications, 348 (2005), 481-495. https://doi.org/10.1016/j.physa.2004.09.033.
14. Zheng B., Moulines E., Abergel F. Price Jump Prediction in a Limit Order Book, Journal of Mathematical Finance, 3:2 (2013), 242-255. https://doi.org/10.4236/jmf.2013.32024.
15. Fletcher T., Shawe-Taylor J. Multiple Kernel Learning with Fisher Kernels for High Frequency Currency Prediction, Comput. Econ., 42 (2013), 217–240. https://doi.org/10.1007/s10614-012-9317-z.
16. Kercheval A.N., Zhang Y. Modelling high-frequency limit order book dynamics with support vector machines, Quantitative Finance, 15 (2015), 1315-1329. https://doi.org/10.1080/14697688.2015.1032546.
17. Platania F., Serrano P., Tapia M. Modelling the shape of the limit order book, Quantitative Finance, 18 (2018), 1575-1597. https://doi.org/10.1080/14697688.2018.1433312.
18. Brogaard J., Hendershott T., Riordan R. Price Discovery without Trading: Evidence from Limit Orders, The Journal of Finance, 74 (2019), 1621-1658. https://doi.org/10.1111/jofi.12769.
