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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.06.031 Byline: Adonis Yatchew (a), Wolfgang Hardle (b) Abstract: The economic theory of option pricing imposes constraints on the structure of call functions and state price densities. Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions (such as monotonicity and convexity) within a single least squares procedure. The bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints. We apply the techniques to option pricing data on the DAX. Author Affiliation: (a) Department of Economics, University of Toronto, 150 St. George St., Toronto, Canada M5S 3G7 (b) Humboldt-Universitat zu Berlin, Center for Applied Statistics and Economics, Germany

We suggest a new method, with very wide applicability, for testing semiparametric hypotheses about functions such as regression means and probability densities. The technique is based on characterising hypotheses in terms of functionals which can be estimated root-n consistently, and constructing test statistics in terms of estimators of the functionals. Since the tests are semiparametric it is appropriate to assess them on the basis of their ability to detect departures of size [n.sup.-1/2] from the null hypothesis. We show that they do indeed have this property. Unlike tests constructed in a nonparametric setting their power does not depend critically on choice of a bandwidth, and in particular, smoothing parameter selection is not an issue that has to be addressed by users of the tests. Bootstrap methods are suggested for calibrating the tests. In a regression setting, applications include tests of specification (such as partial linear and index models) against nonparametric or semiparametric alternatives, and tests of monotonicity, concavity, separability, equality of regression functions and base-independence of equivalence scales. In a density setting, they include tests of radial symmetry and stochastic dominance. JEL classification: C14; D31 Keywords: Bootstrap; Convexity; Curve estimation; Density estimation; Independence; Index model; Monotonicity; Nonparametric; Parametric; Partial linear model; Positivity; Radial symmetry; Regression; Separability; Smoothing

This paper emphasizes the use of data-driven techniques to discern trends in commodity prices. Whereas many previous papers rely on parametric assumptions, we take as our departure point the view that such trends are inherently nonparametric, driven by complex forces of innovation and obsolescence, competition and strategic behavior, resource depletion and discovery, and supply and demand. Our reference specification is the partial linear model yt = f(t) + ztβ + ϵt where macroeconomic variables z enter parametrically, and f is nonparametric, to be discovered using cross-validation.We analyze data on 11 commodities—3 hydrocarbons and 8 metals. For the majority of these commodities, our data-driven estimates of f bear close similarity to band pass estimates which include long term trends and super cycles. The OPEC effect is estimated to have increased oil prices by over 50% on average and coal prices by about 25%. U.S. coal mining legislation is estimated to have increased coal prices by 9% to 15%. [ABSTRACT FROM AUTHOR]