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Weighted-indexed semi-Markov models for modeling financial returns

  • Guglielmo D'Amico
  • Filippo Petroni

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.

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File URL: http://arxiv.org/pdf/1205.2551
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Paper provided by arXiv.org in its series Papers with number 1205.2551.

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Date of creation: May 2012
Date of revision: Jun 2012
Publication status: Published in J. Stat. Mech., P07015, 2012
Handle: RePEc:arx:papers:1205.2551
Contact details of provider: Web page: http://arxiv.org/

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  1. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
  2. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
  3. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
  4. F. Petroni & M. Serva, 2003. "Spot foreign exchange market and time series," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 34(4), pages 495-500, August.
  5. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259, arXiv.org, revised Dec 2011.
  6. M. H. Jensen & A. Johansen & F. Petroni & I. Simonsen, 2004. "Inverse Statistics in the Foreign Exchange Market," Papers cond-mat/0402591, arXiv.org, revised Mar 2004.
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