IDEAS home Printed from https://ideas.repec.org/p/hum/wpaper/sfb649dp2010-003.html
   My bibliography  Save this paper

Uniform confidence bands for pricing kernels

Author

Listed:
  • Wolfgang Karl Härdle
  • Yarema Okhrin
  • Weining Wang

Abstract

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

Suggested Citation

  • Wolfgang Karl Härdle & Yarema Okhrin & Weining Wang, 2010. "Uniform confidence bands for pricing kernels," SFB 649 Discussion Papers SFB649DP2010-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2010-003
    as

    Download full text from publisher

    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-003.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    3. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2008. "State Dependence Can Explain the Risk Aversion Puzzle," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 973-1011, April.
    4. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    5. Maria Grith & Wolfgang Härdle & Juhyun Park, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers SFB649DP2009-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    7. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    8. 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.
    9. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    10. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    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. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
    3. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    6. repec:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500418 is not listed on IDEAS
    7. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    8. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Brendan K. Beare & Lawrence D. W. Schmidt, 2016. "An Empirical Test of Pricing Kernel Monotonicity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 338-356, March.
    10. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    11. Denis Belomestny & Shujie Ma & Wolfgang Karl Härdle, 2015. "Pricing Kernel Modeling," SFB 649 Discussion Papers SFB649DP2015-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Yuri Golubev & Wolfgang Härdle & Roman Timofeev, 2014. "Testing monotonicity of pricing kernels," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 305-326, October.
    13. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Wolfgang Karl Härdle & Rouslan Moro & Linda Hoffmann, 2010. "Learning Machines Supporting Bankruptcy Prediction," SFB 649 Discussion Papers SFB649DP2010-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    16. Carolin Hecht & Katja Hanewald, 2010. "Sociodemographic, Economic, and Psychological Drivers of the Demand for Life Insurance: Evidence from the German Retirement Income Act," SFB 649 Discussion Papers SFB649DP2010-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. Alexander L. Baranovski, 2010. "Dynamical systems forced by shot noise as a new paradigm in the interest rate modeling," SFB 649 Discussion Papers SFB649DP2010-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Audrino, Francesco & Meier, Pirmin, 2012. "Empirical pricing kernel estimation using a functional gradient descent algorithm based on splines," Economics Working Paper Series 1210, University of St. Gallen, School of Economics and Political Science.
    20. Maria Grith & Wolfgang Karl Härdle & Volker Krätschmer, 2013. "Reference Dependent Preferences and the EPK Puzzle," SFB 649 Discussion Papers SFB649DP2013-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    21. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Empirical Pricing Kernel; Confidence band; Bootstrap; Kernel Smoothing; Nonparametric;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hum:wpaper:sfb649dp2010-003. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team). General contact details of provider: http://edirc.repec.org/data/sohubde.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.