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Testing monotonicity of pricing kernels

Author

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  • Yuri Golubev

    ()

  • Wolfgang Härdle

    ()

  • Roman Timofeev

    ()

Abstract

The behaviour of market agents has been extensively covered in the literature. Risk averse behaviour, described by Von Neumann and Morgenstern (Theory of games and economic behavior. Princeton University Press, Princeton, 1944 ) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over an uncertain choice with the same expected value, however, lately there has been a lot of discussion about the empirical evidence of such risk averse behaviour. Some authors have shown that there are regions where market utility functions are locally convex. In this paper we construct a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotonically decreasing EPK corresponds to a concave utility function while a not monotonically decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigate the EPKs for German DAX data for the years 2000, 2002 and 2004 and find evidence of non-concave utility functions: the null hypothesis of a monotonically decreasing pricing kernel is rejected for the data under consideration. The test is based on approximations of spacings through exponential random variables. In a simulation we investigate its performance and calculate the critical values (surface). Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
  • Handle: RePEc:spr:alstar:v:98:y:2014:i:4:p:305-326
    DOI: 10.1007/s10182-014-0225-5
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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.
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    3. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277, March.
    6. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    7. 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.
    8. Wolfgang Karl Härdle & Yarema Okhrin & Weining Wang, 2010. "Uniform confidence bands for pricing kernels," SFB 649 Discussion Papers SFB649DP2010-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Citations

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    Cited by:

    1. 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.
    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. Denis Belomestny & Shujie Ma & Wolfgang Karl Härdle, 2015. "Pricing Kernel Modeling," SFB 649 Discussion Papers SFB649DP2015-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    5. Xinyu WU & Senchun REN & Hailin ZHOU, 2017. "Empirical Pricing Kernels: Evidence from the Hong Kong Stock Market," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 263-278.

    More about this item

    Keywords

    Monotonicity; Pricing kernel; Risk aversion; C12; G12;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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