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Fourier estimation of stochastic leverage using high frequency data

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  • Imma Valentina Curato

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    (Dipartimento di Economia e Management, Universita' degli Studi di Pisa)

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    Abstract

    In this paper, we define a new estimator of the leverage stochastic process based only on a pre-estimation of the Fourier coefficients of the volatility process. This feature constitutes a novelty in comparison with the leverage estimators proposed in the literature generally based on a pre-estimation of the spot volatility. Our estimator is proved to be consistent and in virtue of its definition it can be directly applied to estimate the leverage effect in case of irregular trading observations of the price path and microstructure noise contaminations.

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    Bibliographic Info

    Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2013-04.

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    Length: 19 pages
    Date of creation: Jun 2013
    Date of revision:
    Handle: RePEc:flo:wpaper:2013-04

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    Related research

    Keywords: leverage; non-parametric estimation; semi-martingale; Fourier transform; high frequency data.;

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    References

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    1. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
    3. Peter Carr & Liuren Wu, 2004. "Stochastic Skew in Currency Options," Finance, EconWPA 0409014, EconWPA.
    4. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers, Toulouse - GREMAQ 95.400, Toulouse - GREMAQ.
    5. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    7. Maria Elvira Mancino & Simona Sanfelici, 2011. "Estimation of Quarticity with High Frequency Data," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2011-06, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Jan 2012.
    8. 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.
    9. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
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