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Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach

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  • Constantinides, A.
  • Savel’ev, S.E.

Abstract

ARCH and GARCH stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with Gaussian conditional probability. It can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a Truncated Lévy Flight or GARCH model, but each with individual shortfalls. In this paper therefore, we combine the GARCH process with a conditional truncated Lévy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons.

Suggested Citation

  • Constantinides, A. & Savel’ev, S.E., 2013. "Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2072-2078.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:2072-2078
    DOI: 10.1016/j.physa.2013.01.003
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    Cited by:

    1. Liu, Xueyong & An, Haizhong & Huang, Shupei & Wen, Shaobo, 2017. "The evolution of spillover effects between oil and stock markets across multi-scales using a wavelet-based GARCH–BEKK model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 374-383.
    2. De Clerk, Luke & Savel’ev, Sergey, 2022. "AI algorithms for fitting GARCH parameters to empirical financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    3. Yanlin Shi & Lingbing Feng & Tong Fu, 2020. "Markov Regime-Switching in-Mean Model with Tempered Stable Distribution," Computational Economics, Springer;Society for Computational Economics, vol. 55(4), pages 1275-1299, April.
    4. Lingbing Feng & Yanlin Shi, 2017. "A simulation study on the distributions of disturbances in the GARCH model," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1355503-135, January.
    5. Pokhilchuk, K.A. & Savel’ev, S.E., 2016. "On the choice of GARCH parameters for efficient modelling of real stock price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 248-253.
    6. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    7. Mohammadi, M. & Rezakhah, S. & Modarresi, N., 2020. "Semi-Lévy driven continuous-time GARCH process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    8. Feng Lingbing & Shi Yanlin, 2020. "Markov regime-switching autoregressive model with tempered stable distribution: simulation evidence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(1), pages 1-27, February.
    9. Shi, Yanlin & Feng, Lingbing, 2016. "A discussion on the innovation distribution of the Markov regime-switching GARCH model," Economic Modelling, Elsevier, vol. 53(C), pages 278-288.

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