Abadir, K.M. and Rockinger, M. (2003) Density functionals, with an option-pricing application. Econometric Theory. pp. 778-811. ISSN 0266-4666Full text available as:
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.
|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:||25 Apr 2015 10:45|