Sentiment Lost: the E ect of Projecting the Empirical Pricing Kernel onto a Smaller Filtration Set

This paper analyzes the impacts of using a suboptimal information set for the estimation of the empirical pricing kernel.Not sharing the same nullset, an option-based risk-neutral and a stock-based real world measure lead... [ view full abstract ]

This paper analyzes the impacts of using a suboptimal information set for the estimation of the empirical pricing kernel.

Not sharing the same nullset, an option-based risk-neutral and a stock-based real world measure lead to a distorted the investor's risk premium. The relative empirical pricing kernel is then no longer a true martingale, but a strict local martingale with consequences on the validity of the risk-neutral pricing. From a probabilistic viewpoints, the missing beliefs are totally unaccessible stopping times on the coarser filtration set, so that an absolutely continuous strict local martingale, once projected, becomes continuous with jumps.