We model the dynamics of asset prices and associated derivatives by considerationof the dynamics of the conditional probability density process for the value of an assetat some specied time in the future. In the case where the asset is driven by Brownianmotion, an associated \master equation"...

We provide a new method to derive the state price density per unit probabilitybased on option prices and GARCH model. We derive the risk neutraldistribution using the result in Breeden and Litzenberger (1978) and thehistorical density adapting the GARCH model of Barone-Adesi, Engle, andMancini...