Abstract
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.
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References
Alfi, V., Cristelli, M., Pietronero, L., Zaccaria, A.: Minimal agent based model for financial markets i — origin and self-organization of stylized facts. The European Physical Journal B 67(3), 13 pages (2009). DOI 10.1140/epjb/e2009-00028-4
Bacry, E.: Modeling microstructure noise using point processes. In: Finance and Statistics (Fiesta) Seminar, Ecole Polytechnique (2010)
Bauwens, L., Hautsch, N.: Modelling financial high frequency data using point processes. In: Handbook of Financial Time Series, pp. 953–979 (2009)
Biais, B., Hillion, P., Spatt, C.: An empirical analysis of the limit order book and the order flow in the paris bourse. The Journal of Finance 50(5), 1655–1689 (1995). URL http://www.jstor.org/stable/2329330
Bowsher, C.G.: Modelling security market events in continuous time: Intensity based, multivariate point process models. Journal of Econometrics 141(2), 876–912 (2007). DOI 10.1016/j.jeconom.2006.11.007. URL http://www.sciencedirect.com/science/article/B6VC0-4MV1P46-1/2/2b2c30c69257dc531c7f90517586b771
Chakraborti, A., Muni Toke, I., Patriarca, M., Abergel, F.: Econophysics: Empirical facts and agent-based models. 0909.1974 (2009). URL http://arxiv.org/abs/0909.1974
Challet, D., Stinchcombe, R.: Analyzing and modeling 1+ 1d markets. Physica A: Statistical Mechanics and its Applications 300(1–2), 285–299 (2001)
Cont, R., Bouchaud, J.-P.: Herd behavior and aggregate fluctuations in financial markets. Macroeconomic Dynamics 4(02), 170–196 (2000)
Cont, R., Stoikov, S., Talreja, R.: A Stochastic Model for Order Book Dynamics. SSRN eLibrary(2008)
Engle, R.F.: The econometrics of Ultra-High-Frequency data. Econometrica 68(1), 1–22 (2000). URL http://www.jstor.org/stable/2999473
Engle, R.F., Russell, J.R.: Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model. Journal of Empirical Finance 4(2–3), 187–212 (1997). DOI 10.1016/S0927-5398(97)00006-6. URL http://www.sciencedirect.com/science/article/B6VFG-3SX0D5B-5/2/709b3c532191afd84b0dbffd14b040d8
Hall, A.D., Hautsch, N.: Modelling the buy and sell intensity in a limit order book market. Journal of Financial Markets 10(3), 249–286 (2007). DOI 10.1016/j.finmar.2006.12.002. URL http://www.sciencedirect.com/science/article/B6VHN-4MT5K6F-1/2/1a71db7f8aab72c017e407033edc5734
Hautsch, N.: Modelling irregularly spaced financial data. Springer (2004)
Hawkes, A.G.: Spectra of some self-exciting and mutually exciting point processes. Biometrika 58(1), 83–90 (1971). DOI 10.1093/biomet/58.1.83. URL http://biomet.oxfordjournals.org/cgi/content/abstract/58/1/83
Hawkes, A.G., Oakes, D.: A cluster process representation of a Self-Exciting process. Journal of Applied Probability 11(3), 493–503 (1974). URL http://www.jstor.org/stable/3212693
Hewlett, P.: Clustering of order arrivals, price impact and trade path optimisation. In: Workshop on Financial Modeling with Jump processes, Ecole Polytechnique (2006)
Large, J.:Measuring the resiliency of an electronic limit order book. Journal of Financial Markets 10(1), 1–25 (2007). DOI 10.1016/j.finmar.2006.09.001. URL http://www.sciencedirect.com/science/article/B6VHN-4M936YC-1/2/45b513a31fc6df3b6921987eaafded84
Lux, T., Marchesi, M., Italy, G.: Volatility clustering in financial markets. Int. J. Theo. Appl. Finance 3, 675–702 (2000)
Mike, S., Farmer, J.D.: An empirical behavioral model of liquidity and volatility. Journal of Economic Dynamics and Control 32(1), 200–234 (2008)
Ogata, Y.: On Lewis’ simulation method for point processes. IEEE Transactions on Information Theory 27(1), 23–31 (1981)
Preis, T., Golke, S., Paul, W., Schneider, J.J.: Multi-agent-based order book model of financial markets. EPL (Europhysics Letters) 75(3), 510–516 (2006). URL http://www.iop.org/EJ/abstract/0295-5075/75/3/510/
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Toke, I.M. (2011). “Market Making” in an Order Book Model and Its Impact on the Spread. In: Abergel, F., Chakrabarti, B.K., Chakraborti, A., Mitra, M. (eds) Econophysics of Order-driven Markets. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-1766-5_4
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DOI: https://doi.org/10.1007/978-88-470-1766-5_4
Publisher Name: Springer, Milano
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