Polynomial Jump-Diffusion Models
40 Pages Posted: 27 Nov 2017 Last revised: 22 Jul 2019
Date Written: January 2, 2019
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.
Keywords: polynomial jump-diffusions, affine jump-diffusions, polynomial transformations, conditional Lévy processes, Lévy time change, asset pricing models, stochastic volatility
JEL Classification: G12, G13
Suggested Citation: Suggested Citation