The information premium on a finite probability space

Abstract

On a finite probability space, we consider a problem of {\it fair pricing} of contingent claims in the sense of \cite{FS89} and its sensitivity to a distortion of information, where we follow the {\it weak information} modeling approach from \cite{Fabrice03}. We show that, in complete models, or more generally, for replicable contingent claims, the weak information does not affect the fair price. For incomplete models, this is not the case for non-replicable claims, where we obtain explicit formulas for the {\it information premium} and {\it correction to an optimal trading strategy}. We illustrate our results by an example, where we demonstrate that under weak information, the fair price can increase, stay the same, or decrease. Finally, we perform the stability analysis for the information premium and the correction of the optimal trading strategy to perturbations of the contingent claim payoff, stock price dynamics, and the reference probability measure.