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Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models

Author

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  • Emanuele Taufer

    (DISA, Faculty of Economics, Trento University)

  • Nikolai Leonenko
  • Marco Bee

Abstract

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a real-data application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.

Suggested Citation

  • Emanuele Taufer & Nikolai Leonenko & Marco Bee, 2009. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," DISA Working Papers 0907, Department of Computer and Management Sciences, University of Trento, Italy, revised 02 Dec 2009.
    • Handle: RePEc:trt:disawp:0907
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    References listed on IDEAS

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    Cited by:

    1. Nikolai Leonenko & EStuart Petherick & Emanuele Taufer, 2012. "Multifractal Scaling for Risky Asset Modelling," DISA Working Papers 2012/07, Department of Computer and Management Sciences, University of Trento, Italy, revised Jul 2012.
    2. Szczepocki Piotr, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Statistics Poland, vol. 21(2), pages 173-187, June.
    3. Kotchoni, Rachidi, 2014. "The indirect continuous-GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 464-488.
    4. Leonenko, Nikolai & Petherick, Stuart & Taufer, Emanuele, 2013. "Multifractal models via products of geometric OU-processes: Review and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 7-16.
    5. Stelzer Robert & Tosstorff Thomas & Wittlinger Marc, 2015. "Moment based estimation of supOU processes and a related stochastic volatility model," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 1-24, April.
    6. Stojanović, Vladica S. & Popović, Biljana Č. & Milovanović, Gradimir V., 2016. "The Split-SV model," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 560-581.
    7. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    8. Bruno Ebner & Bernhard Klar & Simos G. Meintanis, 2018. "Fourier inference for stochastic volatility models with heavy-tailed innovations," Statistical Papers, Springer, vol. 59(3), pages 1043-1060, September.

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    Keywords

    ornstein-uhlenbeck process; lévy process; stochastic volatility; characteristic function estimation;
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