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Efficient Derivative Pricing by the Extended Method of Moments

Author

Listed:
  • 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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Suggested Citation

  • P. Gagliardini & C. Gourieroux & E. Renault, 2011. "Efficient Derivative Pricing by the Extended Method of Moments," Econometrica, Econometric Society, vol. 79(4), pages 1181-1232, July.
  • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:4:p:1181-1232
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    Cited by:

    1. Jarrow, Robert & Kwok, Simon Sai Man, 2015. "Specification tests of calibrated option pricing models," Journal of Econometrics, Elsevier, vol. 189(2), pages 397-414.
    2. Gianluca Cassese, 2015. "Nonparametric Estimates of Option Prices Using Superhedging," Working Papers 293, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    3. Francesco Audrino & Dominik Colangelo, 2009. "Option trading strategies based on semi-parametric implied volatility surface prediction," University of St. Gallen Department of Economics working paper series 2009 2009-24, Department of Economics, University of St. Gallen.
    4. 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.
    5. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    6. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    7. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    8. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    9. Zhentao Shi & Huanhuan Zheng, 2018. "Structural Estimation of Behavioral Heterogeneity," Papers 1802.03735, arXiv.org.
    10. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
    11. Majewski, Adam A. & Bormetti, Giacomo & Corsi, Fulvio, 2015. "Smile from the past: A general option pricing framework with multiple volatility and leverage components," Journal of Econometrics, Elsevier, vol. 187(2), pages 521-531.
    12. Torben G. Andersen & Nicola Fusari & Viktor Todorov & Rasmus T. Varneskov, 1001. "Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span," CREATES Research Papers 2018-03, Department of Economics and Business Economics, Aarhus University.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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