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Modeling the coupled return-spread high frequency dynamics of large tick assets

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  • Gianbiagio Curato
  • Fabrizio Lillo
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    Abstract

    Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a Markov-switching modeling approach for price change, where the latent Markov process is the transition between spreads. We then use a finite Markov mixture of logit regressions on past squared returns to describe the dependence of the probability of price changes. The model can thus be seen as a Double Chain Markov Model. We show that the model describes the shape of return distribution at different time aggregations, volatility clustering, and the anomalous decrease of kurtosis of returns. We calibrate our models on Nasdaq stocks and we show that this model reproduces remarkably well the statistical properties of real data.

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    File URL: http://arxiv.org/pdf/1310.4539
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    Paper provided by arXiv.org in its series Papers with number 1310.4539.

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    Date of creation: Oct 2013
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    Handle: RePEc:arx:papers:1310.4539

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    1. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
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    4. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    5. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
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    7. Zolt�n Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    8. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Working Papers hal-00603385, HAL.
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    10. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    11. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    12. Onnela, Jukka-Pekka & Töyli, Juuso & Kaski, Kimmo, 2009. "Tick size and stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 441-454.
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