Efficient Derivative Pricing by the Extended Method of Moments

55 Pages Posted: 10 Feb 2010

See all articles by Patrick Gagliardini

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)

Eric Renault

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

Date Written: October 1, 2009

Abstract

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 for reconstructing the pricing operator at 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 large time series dimension, but 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.

Keywords: Derivative Pricing, Trading Activity, GMM, Information Theoretic Estimation, KLIC, Identification, Weak Instrument, Nonparametric Efficiency, Semiparametric Efficiency

JEL Classification: C13, C14, G12

Suggested Citation

Gagliardini, Patrick and Gourieroux, Christian and Renault, Eric, Efficient Derivative Pricing by the Extended Method of Moments (October 1, 2009). Swiss Finance Institute Research Paper No. 10-07. Available at SSRN: https://ssrn.com/abstract=1550135 or http://dx.doi.org/10.2139/ssrn.1550135

Patrick Gagliardini (Contact Author)

USI Università della Svizzera italiana ( email )

Via Buffi 13
Lugano, TN 6900
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
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Switzerland

Christian Gourieroux

University of Toronto - Department of Economics ( email )

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

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

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Montreal, Quebec H3C 3J7
Canada

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

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92245 Malakoff Cedex
France
33.4117.7666 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Eric Renault

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

Chapel Hill, NC 27599
United States

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