IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v157y2010i2p257-271.html
   My bibliography  Save this article

Nonparametric estimation for a class of Lévy processes

Author

Listed:
  • Chen, Song X.
  • Delaigle, Aurore
  • Hall, Peter

Abstract

We consider estimation for a class of Lévy processes, modelled as a sum of a drift, a symmetric stable process and a compound Poisson process. We propose a nonparametric approach to estimating unknown parameters of our model, including the drift, the scale and index parameters in the stable law, the mean of the Poisson process and the underlying jump size distribution. We show that regression and nonparametric deconvolution methods, based on the empirical characteristic function, can be used for inference. Interesting connections are shown to exist between properties of our estimators and of those found in conventional deconvolution.

Suggested Citation

  • Chen, Song X. & Delaigle, Aurore & Hall, Peter, 2010. "Nonparametric estimation for a class of Lévy processes," Journal of Econometrics, Elsevier, vol. 157(2), pages 257-271, August.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:257-271
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00002-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    3. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    4. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    5. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    6. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    7. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    8. Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, July.
    9. Woerner, Jeannette H.C., 2004. "Estimating The Skewness In Discretely Observed Lévy Processes," Econometric Theory, Cambridge University Press, vol. 20(5), pages 927-942, October.
    10. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
    11. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    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. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "A data-driven framework for consistent financial valuation and risk measurement," European Journal of Operational Research, Elsevier, vol. 289(1), pages 381-398.
    2. Kato, Kengo & Kurisu, Daisuke, 2020. "Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1159-1205.
    3. Shota Gugushvili & Bert van Es & Peter Spreij, 2011. "Deconvolution for an atomic distribution: rates of convergence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1003-1029.
    4. Fabienne Comte & Céline Duval & Valentine Genon-Catalot, 2014. "Nonparametric density estimation in compound Poisson processes using convolution power estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 163-183, January.

    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. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    2. Rama Cont & Peter Tankov, 2009. "Constant Proportion Portfolio Insurance In The Presence Of Jumps In Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 379-401, July.
    3. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    4. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    5. Laurens Haan & Cécile Mercadier & Chen Zhou, 2016. "Adapting extreme value statistics to financial time series: dealing with bias and serial dependence," Finance and Stochastics, Springer, vol. 20(2), pages 321-354, April.
    6. Goegebeur, Yuri & Guillou, Armelle & Pedersen, Tine & Qin, Jing, 2022. "Extreme-value based estimation of the conditional tail moment with application to reinsurance rating," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 102-122.
    7. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    8. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    9. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    10. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.
    11. Jakob Sohl, 2012. "Confidence sets in nonparametric calibration of exponential L\'evy models," Papers 1202.6611, arXiv.org, revised Sep 2013.
    12. repec:hum:wpaper:sfb649dp2012-012 is not listed on IDEAS
    13. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    14. Liu, Qing & Peng, Liang & Wang, Xing, 2017. "Haezendonck–Goovaerts risk measure with a heavy tailed loss," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 28-47.
    15. Todorov, Viktor, 2022. "Nonparametric jump variation measures from options," Journal of Econometrics, Elsevier, vol. 230(2), pages 255-280.
    16. repec:hum:wpaper:sfb649dp2012-017 is not listed on IDEAS
    17. Wagner, Niklas & Marsh, Terry A., 2005. "Measuring tail thickness under GARCH and an application to extreme exchange rate changes," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 165-185, January.
    18. Söhl, Jakob, 2012. "Confidence sets in nonparametric calibration of exponential Lévy models," SFB 649 Discussion Papers 2012-012, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    20. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    21. Koning, A.J. & Peng, L., 2005. "Goodness-of-fit tests for a heavy tailed distribution," Econometric Institute Research Papers EI 2005-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    22. Trabs, Mathias, 2011. "Calibration of self-decomposable Lévy models," SFB 649 Discussion Papers 2011-073, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    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:eee:econom:v:157:y:2010:i:2:p:257-271. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.