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Measure preserving derivatives and the pricing kernel puzzle

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  • Beare, Brendan K.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 6 ()
    Pages: 689-697

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:689-697

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Hardy–Littlewood inequality; Payoff distribution pricing model; Pricing kernel puzzle; Ryff’s decomposition;

    References

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    18. Beare, Brendan K. & Schmidt, Lawrence, 2011. "An Empirical Test of Pricing Kernel Monotonicity," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt5572n8pc, Department of Economics, UC San Diego.
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    20. Yuri Golubev & Wolfgang Härdle & Roman Timonfeev, 2008. "Testing Monotonicity of Pricing Kernels," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2008-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:
    1. Beare, Brendan K. & Schmidt, Lawrence, 2011. "An Empirical Test of Pricing Kernel Monotonicity," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt5572n8pc, Department of Economics, UC San Diego.
    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, Department of Economics, UC San Diego qt6qg1f8ms, Department of Economics, UC San Diego.

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