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Density functionals, with an option-pricing application

Abadir, K.M. and Rockinger, M. (2003) Density functionals, with an option-pricing application. Econometric Theory. pp. 778-811. ISSN 0266-4666

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We present a method of estimating density-related functionals, without prior knowledge of the density’s functional form. The approach revolves around the specification of an explicit formula for a new class of distributions that encompasses many of the known cases in statistics, including the normal, gamma, inverse gamma, and mixtures thereof. The functionals are based on a couple of hypergeometric functions. Their parameters can be estimated, and the estimates then reveal both the functional form of the density and the parameters that determine centering, scaling, etc. The function to be estimated always leads to a valid density, by design, namely, one that is nonnegative everywhere and integrates to 1. Unlike fully nonparametric methods, our approach can be applied to small datasets. To illustrate our methodology, we apply it to finding risk-neutral densities associated with different types of financial options. We show how our approach fits the data uniformly very well. We also find that our estimated densities’ functional forms vary over the dataset, so that existing parametric methods will not do uniformly well.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 Cambridge University Press
Institution: The University of York
Academic Units: The University of York > Economics and Related Studies (York)
Depositing User: Sherpa Assistant
Date Deposited: 19 Aug 2005
Last Modified: 05 Jun 2016 07:21
Published Version: http://dx.doi.org/10.1017/S0266466603195047
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/588

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