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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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    1. repec:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500418 is not listed on IDEAS
    2. 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.
    3. 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.
    4. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2017. "Mispriced Index Option Portfolios," NBER Working Papers 23708, National Bureau of Economic Research, Inc.
    5. beare, brendan & shi, xiaoxia, 2015. "An improved bootstrap test of density ratio ordering," MPRA Paper 74772, University Library of Munich, Germany.
    6. Denis Belomestny & Shujie Ma & Wolfgang Karl Härdle, 2015. "Pricing Kernel Modeling," SFB 649 Discussion Papers SFB649DP2015-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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