Is the price kernel monotone?

We provide a new method to derive the state price density per unit probability based on option prices and GARCH model. We derive the risk neutral distribution using the result in Breeden and Litzenberger (1978) and the historical density adapting the GARCH model of Barone-Adesi, Engle, and Mancini (2008). We take the ratio of these two probabilities in order to describe the shape of the state price density and to evaluate its consistency with economic theory. We find that using a large dataset and introducing non-Gaussian innovations, the pricing kernel puzzle that arises in Jackwerth (2000) disappears both in a single day and over an average of different days with options expiring at the same maturity. We also evaluate the price kernel at the onset of the recent crisis