Dynamic Nonparametric State Price Density EstimationUsing Constrained Least Squares and the Bootstrap

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.