IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v13y2010i05ns0219024910005991.html
   My bibliography  Save this article

Computation Of Volatility In Stochastic Volatility Models With High Frequency Data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024910005991
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024910005991?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emilio Barucci & Davide Magno & Maria Elvira Mancino, 2012. "Fourier volatility forecasting with high-frequency data and microstructure noise," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 281-293, September.
    2. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    3. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    4. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    5. Torben G. ANDERSEN & Tim BOLLERSLEV & Nour MEDDAHI, 2002. "Correcting The Errors : A Note On Volatility Forecast Evaluation Based On High-Frequency Data And Realized Volatilities," Cahiers de recherche 21-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Jeonggyu Huh, 2018. "Measuring Systematic Risk with Neural Network Factor Model," Papers 1809.04925, arXiv.org.
    7. Corradi, Valentina & Swanson, Norman R., 2005. "Bootstrap specification tests for diffusion processes," Journal of Econometrics, Elsevier, vol. 124(1), pages 117-148, January.
    8. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    9. Daisuke Nagakura & Toshiaki Watanabe, 2015. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 45-82.
    10. Andreou, Elena, 2016. "On the use of high frequency measures of volatility in MIDAS regressions," Journal of Econometrics, Elsevier, vol. 193(2), pages 367-389.
    11. Sizova, Natalia, 2011. "Integrated variance forecasting: Model based vs. reduced form," Journal of Econometrics, Elsevier, vol. 162(2), pages 294-311, June.
    12. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics.
    13. Peter Christoffersen & Francis X. Diebold, 2002. "Financial Asset Returns, Market Timing, and Volatility Dynamics," CIRANO Working Papers 2002s-02, CIRANO.
    14. Bonomo, Marco & Garcia, René & Meddahi, Nour & Tédongap, Roméo, 2015. "The long and the short of the risk-return trade-off," Journal of Econometrics, Elsevier, vol. 187(2), pages 580-592.
    15. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    16. Corradi, Valentina & Distaso, Walter & Swanson, Norman R., 2009. "Predictive density estimators for daily volatility based on the use of realized measures," Journal of Econometrics, Elsevier, vol. 150(2), pages 119-138, June.
    17. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    18. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    19. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Inference for Integrated Volatility," Departmental Working Papers 200616, Rutgers University, Department of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:n:s0219024910005991. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.