Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2011, Volume 79, Issue 4

Efficient Derivative Pricing by the Extended Method of Moments
p. 1181-1232

P. Gagliardini, C. Gourieroux, E. Renault

In this paper, we introduce the extended method of moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard generalized method of moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e., valid for any value of the conditioning variable), but also local conditional moment restrictions valid for a given fixed value of the conditioning variable. The local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns. The estimated derivative prices are consistent for a large time series dimension, but a fixed number of cross sectionally observed derivative prices. The asymptotic properties of the XMM estimator are nonstandard, since the combination of uniform and local conditional moment restrictions induces different rates of convergence (parametric and nonparametric) for the parameters.

Log In To View Full Content

Supplemental Material

Supplement to "Efficient Derivative Pricing by the Extended Method of Moments"

This appendix provides the proofs of the theoretical results and technical Lemmas that have been omitted in the paper.

Supplement to "Efficient Derivative Pricing by the Extended Method of Moments"

A zip file containing replication files for the manuscript.