Efficient Derivative Pricing by Extended Method of Moments

72 Pages Posted: 4 Mar 2005

See all articles by Eric Renault

Eric Renault

University of North Carolina (UNC) at Chapel Hill - Department of Economics

Patrick Gagliardini

USI Università della Svizzera italiana; Swiss Finance Institute

Christian Gourieroux

University of Toronto - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE); National Bureau of Economic Research (NBER)

Date Written: January 2005

Abstract

In this paper we consider an incomplete market framework and explain how to use jointly observed prices of the underlying asset and some derivatives written on this asset for an efficient pricing of other derivatives. This question involves two types of moment restrictions, which can be written either for a given value of the conditionning variable , or can be unform with respect to this conditionning variable. This distinction between local and uniform conditional moment restrictions leads to an extension of the Generalized Method of Moments, a method in which all restrictions are assumed uniform. We derive the (kernel) nonparametric efficiency bound for estimating a conditional moment of interest and prove the asymptotic efficiency of the Extended Method of Moments. The general results are applied in a stochastic volatility model to get efficient derivative asset prices.

Keywords: Generalized Method of Moments, Derivative pricing, Stochastic Volatility

JEL Classification: C13, C14, G12

Suggested Citation

Renault, Eric and Gagliardini, Patrick and Gourieroux, Christian, Efficient Derivative Pricing by Extended Method of Moments (January 2005). Available at SSRN: https://ssrn.com/abstract=676108 or http://dx.doi.org/10.2139/ssrn.676108

Eric Renault (Contact Author)

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

Patrick Gagliardini

USI Università della Svizzera italiana ( email )

Via Buffi 13
Lugano, TN 6900
Switzerland

Swiss Finance Institute ( email )

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

Christian Gourieroux

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada
416-978-4349 (Phone)
416-978-6713 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE) ( email )

15 Boulevard Gabriel Peri
92245 Malakoff Cedex
France
33.4117.7666 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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