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

  • Gianbiagio Curato
  • Fabrizio Lillo
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    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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    8. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
    9. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 344-366, Spring.
    10. 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.
    11. 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.
    12. 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.
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