[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v112y2017i520p1744-1758.html
   My bibliography  Save this article

Estimation of the Continuous and Discontinuous Leverage Effects

Author

Listed:
  • Yacine Aït-Sahalia
  • Jianqing Fan
  • Roger J. A. Laeven
  • Christina Dan Wang
  • Xiye Yang
Abstract
This article examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one. Supplementary materials for this article are available online.

Suggested Citation

  • Yacine Aït-Sahalia & Jianqing Fan & Roger J. A. Laeven & Christina Dan Wang & Xiye Yang, 2017. "Estimation of the Continuous and Discontinuous Leverage Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1744-1758, October.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:520:p:1744-1758
    DOI: 10.1080/01621459.2016.1240082
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2016.1240082
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2016.1240082?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. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    2. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    3. Christina D. Wang & Per A. Mykland, 2014. "The Estimation of Leverage Effect With High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 197-215, March.
    4. Bandi, Federico M. & Renò, Roberto, 2012. "Time-varying leverage effects," Journal of Econometrics, Elsevier, vol. 169(1), pages 94-113.
    5. Mathias Vetter, 2012. "Estimation of Correlation for Continuous Semimartingales," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 757-771, December.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 353-384.
    8. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
    9. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    10. Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2015. "Exploring Return Dynamics via Corridor Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2902-2945.
    11. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    12. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    13. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    14. Fan, Yingying & Fan, Jianqing, 2011. "Testing and detecting jumps based on a discretely observed process," Journal of Econometrics, Elsevier, vol. 164(2), pages 331-344, October.
    Full references (including those not matched with items on IDEAS)

    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. Ilze Kalnina & Dacheng Xiu, 2017. "Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 384-396, January.
    2. Bollerslev, Tim & Todorov, Viktor, 2023. "The jump leverage risk premium," Journal of Financial Economics, Elsevier, vol. 150(3).
    3. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    4. Linton, Oliver & Whang, Yoon-Jae & Yen, Yu-Min, 2016. "A nonparametric test of a strong leverage hypothesis," Journal of Econometrics, Elsevier, vol. 194(1), pages 153-186.
    5. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    6. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2017. "Inference on Self‐Exciting Jumps in Prices and Volatility Using High‐Frequency Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 504-532, April.
    7. Curato, Imma Valentina & Sanfelici, Simona, 2022. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Econometrics and Statistics, Elsevier, vol. 23(C), pages 53-82.
    8. 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.
    9. Jacod, Jean & Klüppelberg, Claudia & Müller, Gernot, 2017. "Testing for non-correlation between price and volatility jumps," Journal of Econometrics, Elsevier, vol. 197(2), pages 284-297.
    10. 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.
    11. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    12. Yan Qu & Angelos Dassios & Hongbiao Zhao, 2023. "Shot-noise cojumps: Exact simulation and option pricing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 647-665, March.
    13. Huang, Jing-Zhi & Ni, Jun & Xu, Li, 2022. "Leverage effect in cryptocurrency markets," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    14. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    15. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    16. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    17. Omar Euch & Masaaki Fukasawa & Mathieu Rosenbaum, 2018. "The microstructural foundations of leverage effect and rough volatility," Finance and Stochastics, Springer, vol. 22(2), pages 241-280, April.
    18. Guangying Liu & Meiyao Liu & Jinguan Lin, 2022. "Testing the volatility jumps based on the high frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 669-694, September.
    19. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    20. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:112:y:2017:i:520:p:1744-1758. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.