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Weighted-indexed semi-Markov model: calibration and application to financial modeling

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  • Riccardo De Blasis

    (Marche Polytechnic University)

Abstract

We address the calibration issues of the weighted-indexed semi-Markov chain (WISMC) model applied to high-frequency financial data. Specifically, we propose to automate the discretization of the price returns and the volatility index by using four different approaches, two based on statistical quantities, namely, the quantile and sigma discretization, and two derived by the application of two popular machine learning algorithms, namely the k-means and Gaussian mixture model (GMM). Moreover, by comparing the Bayesian information criterion (BIC) scores, the GMM approach allows for the selection of the number of states of returns and index. An application to Bitcoin prices at 1-min and 1-s intervals shows the validity and usefulness of the proposed discretization approaches. In particular, GMM discretization is well suited for high-frequency returns, whereas the quantile approach works better for low-frequency intervals. Finally, by comparing the results of the Monte Carlo simulation, we show that the WISMC model, applied with the proposed discretization, can reproduce the long-range serial correlation of the squared returns, which is typical of the financial markets and, in particular, the cryptocurrency market.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fininn:v:9:y:2023:i:1:d:10.1186_s40854-022-00418-6
    DOI: 10.1186/s40854-022-00418-6
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    References listed on IDEAS

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    1. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    2. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    3. Guglielmo D'Amico & Filippo Petroni, 2011. "A semi-Markov model with memory for price changes," Papers 1109.4259, arXiv.org, revised Dec 2011.
    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. Christian M Hafner, 2020. "Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 233-249.
    6. Anatoliy Swishchuk & Tyler Hofmeister & Katharina Cera & Julia Schmidt, 2017. "General Semi-Markov Model For Limit Order Books," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-21, May.
    7. Tan, Shay-Kee & Chan, Jennifer So-Kuen & Ng, Kok-Haur, 2020. "On the speculative nature of cryptocurrencies: A study on Garman and Klass volatility measure," Finance Research Letters, Elsevier, vol. 32(C).
    8. Riccardo De Blasis, 2020. "The price leadership share: a new measure of price discovery in financial markets," Annals of Finance, Springer, vol. 16(3), pages 381-405, September.
    9. Pietro Fodra & Huyên Pham, 2015. "Semi-Markov Model for Market Microstructure," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 261-295, July.
    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. Puneet Pasricha & Dharmaraja Selvamuthu & Guglielmo D’Amico & Raimondo Manca, 2020. "Portfolio optimization of credit risky bonds: a semi-Markov process approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-14, December.
    12. 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.
    13. Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
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    More about this item

    Keywords

    Semi-Markov; WISMC; Bitcoin; EWMA; k-means; GMM;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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