Dynamic nonparametric state price density estimation using constrained least squares and the bootstrap

Wolfgang Härdle and Adonis Yatchew

No 2002,16, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: The economic theory of option pricing imposes constraints on the structure of call functions and state price densities (SPDs). 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 within a single least squares procedure thus permitting investigation of a wide variety of model specifications and constraints. Among these we consider monotonicity and convexity of the call function and integration to one of the state price density. The procedure easily accommodates heteroskedasticity of the residuals. Static and dynamic properties can be tested using both asymptotic and bootstrap methods. Our monte carlo simulations suggest that bootstrap confidence intervals are far superior to aymptotic ones particularly when estimating derivatives of the call function. We apply the techniques to option pricing data on the DAX.

Keywords: option pricing; state price density estimation; nonparametric least squares; bootstrap inference; monotonicity; convexity (search for similar items in EconPapers)
Date: 2001
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