Constrained general regression in pseudo-Sobolev spaces with application to option pricing

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