We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

The theory of Lévy models for asset pricing simplifies considerably if one takes a pricing kernel approach, which enables one to bypass market incompleteness issues. The special case of a geometric Lévy model (GLM) with constant parameters can be regarded as a natural generalization of the...