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A semi-Markov model for price returns

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  • Guglielmo D'Amico
  • Filippo Petroni

Abstract

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday return are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorreletion function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.

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  • Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model for price returns," Papers 1103.6143, arXiv.org.
    • Handle: RePEc:arx:papers:1103.6143
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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. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    3. 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.
    4. Giner, Javier & Zakamulin, Valeriy, 2023. "A regime-switching model of stock returns with momentum and mean reversion," Economic Modelling, Elsevier, vol. 122(C).
    5. Filippo Petroni & Maurizio Serva, 2015. "Observability of Market Daily Volatility," Papers 1503.08032, arXiv.org.
    6. Petroni, Filippo & Serva, Maurizio, 2016. "Observability of market daily volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 838-842.
    7. D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
    8. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    9. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    10. Guglielmo D’Amico & Ada Lika & Filippo Petroni, 2019. "Change point dynamics for financial data: an indexed Markov chain approach," Annals of Finance, Springer, vol. 15(2), pages 247-266, June.
    11. D׳Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2015. "Reliability measures for indexed semi-Markov chains applied to wind energy production," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 170-177.
    12. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
    13. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2018. "Indexed Markov Chains for financial data: testing for the number of states of the index process," Papers 1802.01540, arXiv.org.
    14. Dmitrii Silvestrov & Raimondo Manca, 2017. "Reward Algorithms for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1191-1209, December.
    15. Guglielmo D’Amico & Filippo Petroni & Flavio Prattico, 2015. "Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 781-794, September.

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