Returns of claims on the upside and the viability of U-shaped pricing kernels

Abstract

Financial returns at unit time are modeled as non-Gaussian limit laws. They may reflect random walks or additive processes reflecting some predictability. Mixtures of these two constructions are formulated and estimated on one minute data. It is observed that the random walk fraction is generally below 10%. The results argue against a strict random walk in favor of the presence of a predictable component representing returns as perpetual motion machines responding to the larger past price movements.