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Efficient Derivative Pricing By The Extended Method of Moments

Author

Listed:
  • Patrick GAGLIARDINI

    (University of Lugano and Swiss Finance Institute)

  • Christian GOURIEROUX

    (CREST, CEPREMAP (Paris) and University of Toronto)

  • Eric RENAULT

    (CIRANO-CIREQ (Montreal) and University of North Carolina at Chapel Hill)

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.

Suggested Citation

  • Patrick GAGLIARDINI & Christian GOURIEROUX & Eric RENAULT, 2010. "Efficient Derivative Pricing By The Extended Method of Moments," Swiss Finance Institute Research Paper Series 10-07, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1007
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    Keywords

    Derivative Pricing; Trading Activity; GMM; Information Theoretic Estimation; KLIC; Identification; Weak Instrument; Nonparametric Efficiency; Semiparametric Efficiency;
    All these keywords.

    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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