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Computation Of Volatility In Stochastic Volatility Models With High Frequency Data

Author

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  • EMILIO BARUCCI

    (Dipartimento di Matematica, Politecnico di Milano, Italy)

  • MARIA ELVIRA MANCINO

    (DIMAD, Università di Firenze, Italy)

Abstract

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

Suggested Citation

  • Emilio Barucci & Maria Elvira Mancino, 2010. "Computation Of Volatility In Stochastic Volatility Models With High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 767-787.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:n:s0219024910005991
    DOI: 10.1142/S0219024910005991
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    References listed on IDEAS

    as
    1. S. Sanfelici & M. E. Mancino, 2008. "Covariance estimation via Fourier method in the presence of asynchronous trading and microstructure noise," Economics Department Working Papers 2008-ME01, Department of Economics, Parma University (Italy).
    2. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
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    Cited by:

    1. Imma Valentina Curato & Simona Sanfelici, 2019. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Papers 1910.06660, arXiv.org, revised Mar 2021.
    2. Imma Valentina Curato, 2013. "Fourier estimation of stochastic leverage using high frequency data," Working Papers - Mathematical Economics 2013-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    3. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.
    4. Maria Elvira Mancino & Maria Cristina Recchioni, 2015. "Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-33, September.
    5. Curato, Imma Valentina, 2019. "Estimation of the stochastic leverage effect using the Fourier transform method," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3207-3238.
    6. Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2019. "Asymptotic results for the Fourier estimator of the integrated quarticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 471-502, December.
    7. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.

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