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Copula based multivariate semi-Markov models with applications in high-frequency finance

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  • D’Amico, Guglielmo
  • Petroni, Filippo

Abstract

We introduce a new multivariate model of multiple asset returns. Our model is based on weighted indexed semi-Markov chains to describe the single (marginals) asset returns, whereas the dependence structure among the considered assets is described by introducing copula functions. A real application of the proposed multivariate model is presented based on the evolution of 6 stocks from the Italian Stock Exchange. We provide empirical evidence that the model is able to correctly reproduce statistical regularities of multivariate real data such as the cross-correlation function, value-at-risk, marginal value-at-risk and conditional value-at-risk. The model is also used for volatility forecasting of each stock.

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  • 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.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:765-777
    DOI: 10.1016/j.ejor.2017.12.016
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    1. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    2. 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.
    3. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    4. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    5. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    6. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259, arXiv.org, revised Dec 2011.
    7. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    8. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
    9. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    10. Kakouris, Iakovos & Rustem, Berç, 2014. "Robust portfolio optimization with copulas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 28-37.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Pietro Fodra & Huyên Pham, 2015. "Semi-Markov Model for Market Microstructure," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 261-295, July.
    13. 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.
    14. Renata Mansini & Włodzimierz Ogryczak & M. Speranza, 2007. "Conditional value at risk and related linear programming models for portfolio optimization," Annals of Operations Research, Springer, vol. 152(1), pages 227-256, July.
    15. Laih, Yih-Wenn, 2014. "Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm," European Journal of Operational Research, Elsevier, vol. 232(2), pages 375-382.
    16. 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.
    17. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    19. Sak, Halis & Hörmann, Wolfgang & Leydold, Josef, 2010. "Efficient risk simulations for linear asset portfolios in the t-copula model," European Journal of Operational Research, Elsevier, vol. 202(3), pages 802-809, May.
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    1. D’Amico, Guglielmo & Gismondi, Fulvio & Petroni, Filippo & Prattico, Flavio, 2019. "Stock market daily volatility and information measures of predictability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 22-29.
    2. Guglielmo D'Amico & Filippo Petroni & Philippe Regnault & Stefania Scocchera & Loriano Storchi, 2019. "A copula based Markov Reward approach to the credit spread in European Union," Papers 1902.00691, arXiv.org.
    3. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    4. Riccardo De Blasis, 2023. "Weighted-indexed semi-Markov model: calibration and application to financial modeling," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-16, December.
    5. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    6. Guglielmo D’Amico & Giovanni Masala & Filippo Petroni & Robert Adam Sobolewski, 2020. "Managing Wind Power Generation via Indexed Semi-Markov Model and Copula," Energies, MDPI, vol. 13(16), pages 1-21, August.
    7. Mubenga-Tshitaka, Jean-Luc & Muteba Mwamba, John W. & Dikgang, Johane & Gelo, Dambala, 2021. "Risk spillover between climate variables and the agricultural commodity market in East Africa," EconStor Preprints 243160, ZBW - Leibniz Information Centre for Economics.
    8. Anatoliy Swishchuk, 2021. "Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 399-428, March.
    9. Nelson Vadori & Anatoliy Swishchuk, 2019. "Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications," Mathematics, MDPI, vol. 7(5), pages 1-62, May.
    10. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    11. 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.
    12. Xiaohong Wang & Shixiang Li & Lizhi Wang & Yaning Sun & Zhongxing Wang, 2020. "Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State," Energies, MDPI, vol. 13(22), pages 1-25, November.
    13. Manahov, Viktor & Urquhart, Andrew, 2021. "The efficiency of Bitcoin: A strongly typed genetic programming approach to smart electronic Bitcoin markets," International Review of Financial Analysis, Elsevier, vol. 73(C).

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