Constrained General Regression in Pseudo-Sobolev Spaces with Application to Option Pricing

Abstract

State price density (SPD) contains important information concerning market expectations. In existing literature, a constrained estimator of the SPD is found by nonlinear least squares in a suitable Sobolev space. We improve the behavior of this estimator by implementing a covariance structure taking into account the time of the trade and by considering simultaneously both the observed Put and Call option prices.isotonic regression, Sobolev spaces, monotonicity, multiple observations, covariance structure, option price