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Pricing kernel modeling

Author

Listed:
  • Belomestny, Denis
  • Ma, Shujie
  • Härdle, Wolfgang Karl

Abstract

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel density estimator with varying unknown weights for di erent observations, and the subjective density is approximated by a kernel density estimator with equal weights. We represent the European call option price function by the second order integration of the risk-neutral density, so that the unknown weights are obtained through one-step penalized least squares estimation with the Kullback-Leibler divergence as the penalty function. Asymptotic results of the resulting estimators are established. The performance of the proposed method is illustrated empirically by simulation and real data application studies.

Suggested Citation

  • Belomestny, Denis & Ma, Shujie & Härdle, Wolfgang Karl, 2014. "Pricing kernel modeling," SFB 649 Discussion Papers 2015-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2015-001
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    References listed on IDEAS

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    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. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. 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.
    5. 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.
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    Keywords

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    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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