EconPapers    
Economics at your fingertips  
 

DENSITY FUNCTIONALS, WITH AN OPTION-PRICING APPLICATION

Karim Maher Abadir () and Michael Rockinger ()

Econometric Theory, 2003, vol. 19, issue 05, pages 778-811

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 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.We thank Hans-J rg B ttler, Ale ern , Tony Culyer, Les Godfrey, David Hendry, Sam Kotz, Steve Lawford, Peter Phillips, Bas Werker, and three anonymous referees for their comments. We also thank for their feedback the participants at the seminars and conferences where this paper has been invited, in particular the 1998 CEPR Finance Network Workshop, the 1998 METU conference, the 1998 FORC (Warwick) conference Options: Recent Advances, Money Macro Finance Group, the Swiss National Bank, Imperial College, Tilburg University, Universit Libre de Bruxelles, the University of Oxford, Southampton University, and UMIST. The first author acknowledges support from the ESRC (UK) grant R000239538. The second author acknowledges help from the HEC Foundation and the European Community TMR grant Financial Market Efficiency and Economic Efficiency. This paper was written when the second author was affiliated with HEC-Paris.

Date: 2003
References: Add references at CitEc
Citations View citations in EconPapers (13) Track citations by RSS feed

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466603195047 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:19:y:2003:i:05:p:778-811_19

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Keith Waters ().

 
Page updated 2014-03-30
Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:778-811_19