Polynomial jump-diffusion models

Abstract

We develop a comprehensive mathematical framework for polynomial jump diffusions in a semimartingale context, which nest affine jump diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional Lévy based on polynomial jump diffusions.