Density functionals, with an option-pricing application

Détails

ID Serval
serval:BIB_2A5E0D2C211C
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Density functionals, with an option-pricing application
Périodique
Econometric Theory
Auteur⸱e⸱s
Abadir K., Rockinger M.
ISSN
0266-4666
Statut éditorial
Publié
Date de publication
2003
Peer-reviewed
Oui
Volume
19
Numéro
5
Pages
778-811
Langue
anglais
Résumé
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.
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Création de la notice
19/11/2007 10:57
Dernière modification de la notice
20/08/2019 14:10
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