Density Functionals, with an Option-Pricing Application

34 Pages Posted: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Michael Rockinger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne); Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Date Written: 2003

Abstract

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 which 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 centring, 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.

Suggested Citation

Abadir, Karim M. and Rockinger, Georg Michael, Density Functionals, with an Option-Pricing Application (2003). Econometric Theory, Vol. 19, p. 778, 2003. Available at SSRN: https://ssrn.com/abstract=1984828

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Georg Michael Rockinger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland
+41 21 728 3348 (Phone)
+41+21 692 3435 (Fax)

HOME PAGE: http://www.hec.unil.ch/mrockinger

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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