IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v150y2009i1p1-15.html
   My bibliography  Save this article

Dynamics of state price densities

Author

Listed:
  • Härdle, Wolfgang
  • Hlávka, Zdenek

Abstract

State price densities (SPDs) are an important element in applied quantitative finance. In a Black-Scholes world they are lognormal distributions, but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy no-arbitrage constraints and corrects for the intraday covariance structure in option prices. In contrast to existing methods, we do not use any parametric or smoothness assumptions.

Suggested Citation

  • Härdle, Wolfgang & Hlávka, Zdenek, 2009. "Dynamics of state price densities," Journal of Econometrics, Elsevier, vol. 150(1), pages 1-15, May.
    • Handle: RePEc:eee:econom:v:150:y:2009:i:1:p:1-15
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00024-4
    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. Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
    2. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, January.
    3. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
    4. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-824, December.
    8. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    9. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, January.
    10. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    11. Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    13. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
    14. Fengler, Matthias R. & Härdle, Wolfgang Karl & Mammen, Enno, 2005. "A dynamic semiparametric factor model for implied volatility string dynamics," SFB 649 Discussion Papers 2005-020, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, January.
    16. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    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. repec:hum:wpaper:sfb649dp2006-069 is not listed on IDEAS
    2. Karl Härdle, Wolfgang & López-Cabrera, Brenda & Teng, Huei-Wen, 2015. "State price densities implied from weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 106-125.
    3. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    4. Hlávka, Zdeněk & Peésta, Michal, 2006. "Constrained general regression in pseudo-Sobolev spaces with application to option pricing," SFB 649 Discussion Papers 2006-069, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    6. Ostap Okhrin & Stefan Trück, 2015. "Editorial to the special issue on Applicable semiparametrics of computational statistics," Computational Statistics, Springer, vol. 30(3), pages 641-646, September.
    7. Hlavka, Zdenek, 2006. "Fast algorithm for nonparametric arbitrage-free SPD estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2339-2349, December.
    8. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. repec:hal:journl:peer-00834423 is not listed on IDEAS
    10. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.

    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. Thomas Busch, 2008. "Testing the martingale restriction for option implied densities," Review of Derivatives Research, Springer, vol. 11(1), pages 61-81, March.
    2. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Karl Härdle, Wolfgang & López-Cabrera, Brenda & Teng, Huei-Wen, 2015. "State price densities implied from weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 106-125.
    4. repec:hum:wpaper:sfb649dp2010-021 is not listed on IDEAS
    5. repec:hum:wpaper:sfb649dp2013-026 is not listed on IDEAS
    6. repec:hum:wpaper:sfb649dp2005-021 is not listed on IDEAS
    7. Härdle, Wolfgang Karl & Hlávka, Zdeněk, 2005. "Dynamics of state price densities," SFB 649 Discussion Papers 2005-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    9. Grith, Maria & Härdle, Wolfgang Karl & Park, Juhyun, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers 2009-041, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. Li, Yifan & Nolte, Ingmar & Pham, Manh Cuong, 2024. "Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures," Journal of Econometrics, Elsevier, vol. 241(2).
    11. Mikhail Chernov & Eric Ghysels, 1998. "What Data Should Be Used to Price Options?," CIRANO Working Papers 98s-22, CIRANO.
    12. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2019. "Option Implied Risk-Neutral Density Estimation: A Robust and Flexible Method," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 705-728, August.
    13. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    14. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    15. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    16. Ana M. Monteiro & Antonio A. F. Santos, 2020. "Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints," Review of Derivatives Research, Springer, vol. 23(1), pages 41-61, April.
    17. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    18. Hlávka, Zdeněk & Peésta, Michal, 2006. "Constrained general regression in pseudo-Sobolev spaces with application to option pricing," SFB 649 Discussion Papers 2006-069, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    20. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2009. "Option-implied preferences adjustments, density forecasts, and the equity risk premium," Spanish Economic Review, Springer;Spanish Economic Association, vol. 11(2), pages 141-164, June.
    21. repec:hum:wpaper:sfb649dp2006-069 is not listed on IDEAS
    22. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    23. Thomas Mazzoni, 2018. "Asymptotic Expansion of Risk-Neutral Pricing Density," IJFS, MDPI, vol. 6(1), pages 1-26, March.
    24. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.

    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:150:y:2009:i:1:p:1-15. 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.