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Measure preserving derivatives and the pricing kernel puzzle

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  • Beare, Brendan K.
Abstract
Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.

Suggested Citation

  • Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:689-697
    DOI: 10.1016/j.jmateco.2011.09.005
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Denis Belomestny & Wolfgang Karl Härdle & Ekaterina Krymova, 2017. "Sieve Estimation Of The Minimal Entropy Martingale Marginal Density With Application To Pricing Kernel Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-21, September.
    3. Carole Bernard & Jit Seng Chen & Steven Vanduffel, 2014. "Optimal portfolios under worst-case scenarios," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 657-671, April.
    4. Beare, Brendan K. & Moon, Jong-Myun, 2012. "Testing the concavity of an ordinaldominance curve," University of California at San Diego, Economics Working Paper Series qt6qg1f8ms, Department of Economics, UC San Diego.
    5. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    6. 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.
    7. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    8. Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.
    9. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    10. Brendan K. Beare, 2023. "Optimal measure preserving derivatives revisited," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 370-388, April.
    11. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    12. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    13. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    14. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    15. Ricardo Crisóstomo, 2021. "Estimación de probabilidades representativas del mundo real: importancia de los sesgos conductuales," CNMV Documentos de Trabajo CNMV Documentos de Trabaj, CNMV- Comisión Nacional del Mercado de Valores - Departamento de Estudios y Estadísticas.
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    17. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.

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