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Weighted-indexed semi-Markov models for modeling financial returns

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  • Guglielmo D'Amico
  • Filippo Petroni

Abstract

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.

Suggested Citation

  • Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
  • Handle: RePEc:arx:papers:1205.2551
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    File URL: http://arxiv.org/pdf/1205.2551
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    References listed on IDEAS

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    1. D’Amico, Guglielmo & Petroni, Filippo, 2012. "A semi-Markov model for price returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4867-4876.
    2. F. Petroni & M. Serva, 2003. "Spot foreign exchange market and time series," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(4), pages 495-500, August.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    4. 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.
    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. Jensen, M.H & Johansen, A & Petroni, F & Simonsen, I, 2004. "Inverse statistics in the foreign exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 678-684.
    7. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    8. 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.
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    Citations

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    Cited by:

    1. Guglielmo D'Amico & Filippo Petroni, 2017. "A new approach to the modeling of financial volumes," Papers 1709.05823, arXiv.org.
    2. Filippo Petroni & Maurizio Serva, 2015. "Observability of Market Daily Volatility," Papers 1503.08032, arXiv.org.
    3. Guglielmo D'Amico, 2016. "Generalized semi-Markovian dividend discount model: risk and return," Papers 1605.02472, arXiv.org.
    4. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    5. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    6. Guglielmo D'Amico & Montserrat Guillen & Raimondo Manca & Filippo Petroni, 2017. "Multi-state models for evaluating conversion options in life insurance," Papers 1707.01028, arXiv.org.
    7. Petroni, Filippo & Serva, Maurizio, 2016. "Observability of market daily volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 838-842.
    8. repec:eee:ejores:v:267:y:2018:i:2:p:765-777 is not listed on IDEAS
    9. Jo~ao Pedro Rodrigues do Carmo, 2018. "Modeling stock markets through the reconstruction of market processes," Papers 1803.06653, arXiv.org.
    10. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2014. "Wind speed and energy forecasting at different time scales: A nonparametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 59-66.
    11. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2017. "Insuring wind energy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 542-553.
    12. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.

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