IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i6p1217-1244.html
   My bibliography  Save this article

Spectral estimation of the Lévy density in partially observed affine models

Author

Listed:
  • Belomestny, Denis

Abstract

The problem of estimating the Lévy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the conditional characteristic function of an affine process and local linear smoothing in time. We derive almost sure uniform rates of convergence for the estimated Lévy density both in mixed-frequency and low-frequency setups and prove that these rates are optimal in the minimax sense. Finally, the performance of the estimation algorithms is illustrated in the case of the Bates stochastic volatility model.

Suggested Citation

  • Belomestny, Denis, 2011. "Spectral estimation of the Lévy density in partially observed affine models," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1217-1244, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1217-1244
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(11)00040-8
    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. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    2. Elena Andreou & Eric Ghysels & Andros Kourtellos, 2010. "Forecasting with mixed-frequency data," University of Cyprus Working Papers in Economics 10-2010, University of Cyprus Department of Economics.
    3. Belomestny, Denis, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers 2009-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. 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.
    5. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    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. Nickl, Richard & Reiß, Markus, 2012. "A Donsker theorem for Lévy measures," SFB 649 Discussion Papers 2012-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    3. 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.
    4. repec:hum:wpaper:sfb649dp2012-003 is not listed 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. Richter, Martin & Sørensen, Carsten, 2002. "Stochastic Volatility and Seasonality in Commodity Futures and Options: The Case of Soybeans," Working Papers 2002-4, Copenhagen Business School, Department of Finance.
    2. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    3. repec:wyi:journl:002108 is not listed on IDEAS
    4. George J. Jiang, 2002. "Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest Rates," International Review of Finance, International Review of Finance Ltd., vol. 3(3‐4), pages 233-272, September.
    5. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    6. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    7. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. Li, Junye & Favero, Carlo & Ortu, Fulvio, 2012. "A spectral estimation of tempered stable stochastic volatility models and option pricing," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3645-3658.
    9. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    10. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    11. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    12. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 407-458, Fall.
    13. Michel Culot & Valérie Goffin & Steve Lawford & Sébastien de Meten & Yves Smeers, 2013. "Practical stochastic modelling of electricity prices," Post-Print hal-01021603, HAL.
    14. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    15. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    16. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    17. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    18. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, July.
    19. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    20. Marcin Kacperczyk & Paul Damien & Stephen G. Walker, 2013. "A new class of Bayesian semi-parametric models with applications to option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 967-980, May.
    21. Yan-Feng Wu & Xiangyu Yang & Jian-Qiang Hu, 2024. "Method of Moments Estimation for Affine Stochastic Volatility Models," Papers 2408.09185, arXiv.org.

    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:spapps:v:121:y:2011:i:6:p:1217-1244. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.