Filipovic, DamirLarsson, Martin2021-01-112021-01-112021-01-11202010.2139/ssrn.3075520https://infoscience.epfl.ch/handle/20.500.14299/174571We 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.polynomial jump-diffusionsaffine jump-diffusionspolynomial transformationsconditional Lévy processesLévy time changeasset pricing modelsstochastic volatilitytext::journal::journal article::research article