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Sieve Estimation Of The Minimal Entropy Martingale Marginal Density With Application To Pricing Kernel Estimation

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  • DENIS BELOMESTNY

    (Faculty of Mathematics, Duisburg-Essen University, Thea-Leymann-Str. 9 D-45127 Essen, Germany2National Research University Higher School of Economics, Shabolovka, 26, 119049 Moscow, Russia)

  • WOLFGANG KARL HÄRDLE

    (C.A.S.E. — Center for Applied Statistics and Economics, Humboldt-Universitt zu Berlin, Spandauer Str. 1, 10178 Berlin, Germany4SKBI School of Business, Singapore Management University, 50 Stamford Road, Singapore 178899, Singapore)

  • EKATERINA KRYMOVA

    (Faculty of Mathematics, Duisburg-Essen University, Thea-Leymann-Str. 9 D-45127 Essen, Germany5IITP RAS, Moscow, Russia)

Abstract

We study the problem of nonparametric estimation of the risk-neutral densities from options data. The underlying statistical problem is known to be ill-posed and needs to be regularized. We propose a novel regularized empirical sieve approach for the estimation of the risk-neutral densities which relies on the notion of the minimal martingale entropy measure. The proposed approach can be used to estimate the so-called pricing kernels which play an important role in assessing the risk aversion over equity returns. The asymptotic properties of the resulting estimate are analyzed and its empirical performance is illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500418
    DOI: 10.1142/S0219024917500418
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    References listed on IDEAS

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    Cited by:

    1. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.

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