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Efficient Derivative Pricing by the Extended Method of Moments

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  • P. Gagliardini
  • C. Gourieroux
  • E. Renault

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.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 79 (2011)
Issue (Month): 4 (07)
Pages: 1181-1232

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Handle: RePEc:ecm:emetrp:v:79:y:2011:i:4:p:1181-1232

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Cited by:
  1. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2012. "Parametric Inference and Dynamic State Recovery from Option Panels," NBER Working Papers 18046, National Bureau of Economic Research, Inc.
  2. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
  3. Gianluca Cassese, 2014. "Option pricing in an imperfect world," Working Papers 277, University of Milano-Bicocca, Department of Economics, revised Jun 2014.
  4. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
  5. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.

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