Abstract: This paper extends GMM and information theoretic estimation to settings where the conditional moment restrictions are either uniform (i.e. valid for any value of the conditioning variable), or local (i.e. valid for a particular value of the conditioning variable only). The parameter of interest can be either a structural parameter, or a local conditional moment. This is the framework for option pricing based on both historical data on the underlying asset and cross-sectional data on derivative assets,as a consequence of the rather small traded volumes on derivatives. We derive the asymptotic properties of the estimators and a kernel efficiency bound. The asymptotic behavior is not standard since the speed of convergence depends on the type of parameter considered. The results are applied to the derivative pricing problem using a factor model that is parametric in the stochastic discount factor and non-parametricin the conditional distribution of the observed factors. The extended method of moments is compared with the cross-sectional calibration approach used on the market for pricing S&P 500 options.