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Shape Invariant Modeling of Pricing Kernels and Risk Aversion

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  • Maria Grith
  • Wolfgang Härdle
  • Juhyun Park

Abstract

Several empirical studies reported that pricing kernels exhibit a common pattern across different markets. The main interest in pricing kernels lies in validating the presence of the peaks and their variability in location among curves. Motivated by this observation we investigate the problem of estimating pricing kernels based on the shape invariant model, a semi-parametric approach used for multiple curves with shape-related nonlinear variation. This approach allows us to capture the common features contained in the shape of the functions and at the same time characterize the nonlinear variability with a few interpretable parameters. These parameters provide an informative summary of the curves and can be used to make a further analysis with macroeconomic variables. Implied risk aversion function and utility function can also be derived. The method is demonstrated with the European options and returns values of the German stock index DAX. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

Suggested Citation

  • Maria Grith & Wolfgang Härdle & Juhyun Park, 2013. "Shape Invariant Modeling of Pricing Kernels and Risk Aversion," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 370-399, March.
    • Handle: RePEc:oup:jfinec:v:11:y:2013:i:2:p:370-399
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbs019
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    Citations

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    Cited by:

    1. Barletta, Andrea & Santucci de Magistris, Paolo & Violante, Francesco, 2019. "A non-structural investigation of VIX risk neutral density," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 1-20.
    2. Salim Morched & Ben Mohamed Ezzeddine & Anis Jarboui, 2023. "The impact of innovation type on the performance and social responsibility of French manufacturing companies," Environment Systems and Decisions, Springer, vol. 43(3), pages 433-452, September.
    3. Díaz, Antonio & Esparcia, Carlos, 2021. "Dynamic optimal portfolio choice under time-varying risk aversion," International Economics, Elsevier, vol. 166(C), pages 1-22.
    4. 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.
    5. Gatfaoui, Hayette, 2015. "Pricing the (European) option to switch between two energy sources: An application to crude oil and natural gas," Energy Policy, Elsevier, vol. 87(C), pages 270-283.
    6. Jonathan Dark, 2021. "The lead of oil price rises on US equity market beliefs and preferences," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1861-1887, November.
    7. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    8. Dietmar P. J. Leisen, 2017. "The shape of small sample biases in pricing kernel estimations," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 943-958, June.
    9. Algieri, Bernardina & Leccadito, Arturo & Tunaru, Diana, 2021. "Risk premia in electricity derivatives markets," Energy Economics, Elsevier, vol. 100(C).
    10. Maria Grith & Wolfgang K. Härdle & Alois Kneip & Heiko Wagner, 2016. "Functional Principal Component Analysis for Derivatives of Multivariate Curves," SFB 649 Discussion Papers SFB649DP2016-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    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. Kiesel, Rüdiger & Rahe, Florentin, 2017. "Option pricing under time-varying risk-aversion with applications to risk forecasting," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 120-138.
    13. Liao, Wen Ju & Sung, Hao-Chang, 2020. "Implied risk aversion and pricing kernel in the FTSE 100 index," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    14. 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.
    15. 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.

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