SIEVE ESTIMATION OF THE MINIMAL ENTROPY MARTINGALE MARGINAL DENSITY WITH APPLICATION TO PRICING KERNEL ESTIMATION

Denis Belomestny, Wolfgang Härdle and Ekaterina Krymova
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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
Ekaterina Krymova: Faculty of Mathematics, Duisburg-Essen University, Thea-Leymann-Str. 9 D-45127 Essen, Germany5IITP RAS, Moscow, Russia

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 06, 1-21

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.

Keywords: Pricing kernel; risk neutral density; ill-posed problems; Kullback–Leibler divergence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024917500418

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