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Volatility and realized quadratic variation of differenced returns : A wavelet method approach

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  • Høg, Esben

    ()
    (Department of Business Studies, Aarhus School of Business)

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    Abstract

    This paper analyzes some asymptotic results for an alternative estimator of integrated volatility in a continuous-time diffusion process of high frequency data (used in asset pricing finance). The estimator, which is computationally efficient, is based on the quadratic variation of the second order log-price differences. This is contrary to the well known realized quadratic variation of intra daily returns (which is based on first order log-price differences). This latter is known as realized volatility. Analytically, the asymptotics of the proposed estimator is compared to the usual realized volatility estimators. Lastly, we provide some simulation experiments to illustrate the results.

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    File URL: http://research.asb.dk/fbspretrieve/3418/F_2008_06.PDF
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    Bibliographic Info

    Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Research Group Working Papers with number F-2008-06.

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    Length: 21 pages
    Date of creation: 01 Aug 2008
    Date of revision:
    Handle: RePEc:hhb:aarbfi:2008-06

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    Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
    Fax: + 45 86 15 19 43
    Web page: http://www.asb.dk/about/departments/bs.aspx
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    Related research

    Keywords: continuous-time methods; quadratic variation; realized volatility; second order quadratic variation;

    This paper has been announced in the following NEP Reports:

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    1. Christiansen, Charlotte, 2008. "Level-ARCH short rate models with regime switching: Bivariate modeling of US and European short rates," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 925-948, December.
    2. Asger Lunde & Esben Hoeg, 2003. "Wavelet Estimation of Integrated Volatility," Computing in Economics and Finance 2003 274, Society for Computational Economics.
    3. David C. Porter & Carsten Tanggaard & Daniel G. Weaver & Wei Yu, 2008. "Dispersed Trading and the Prevention of Market Failure: the Case of the Copenhagen Stock Exchange," European Financial Management, European Financial Management Association, vol. 14(2), pages 243-267.
    4. Bartholdy, Jan & Mateus, Cesário, 2006. "Debt and Taxes: Evidence from bank-financed unlisted firms," Finance Research Group Working Papers F-2006-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Anand, Amber & Tanggaard, Carsten & Weaver, Daniel G., 2009. "Paying for Market Quality," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(06), pages 1427-1457, December.
    6. Jan Bartholdy & Dennis Olson & Paula Peare, 2007. "Conducting Event Studies on a Small Stock Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 13(3), pages 227-252.
    7. Christiansen, Charlotte & Joensen, Juanna Schröter & Rangvid, Jesper, 2005. "Do More Economists Hold Stocks?," Finance Research Group Working Papers F-2005-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    9. Consiglio, Andrea & De Giovanni, Domenico, 2007. "Pricing the Option to Surrender in Incomplete Markets," Finance Research Group Working Papers F-2007-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    10. Charlotte Christiansen & Angelo Ranaldo, 2006. "Realized Bond-Stock Correlation: Macroeconomic Announcement Effects," Working Papers 2006-02, Swiss National Bank.
    11. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility of diffusion processes with high frequency data," Economics Letters, Elsevier, vol. 74(3), pages 371-378, February.
    12. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    13. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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