Polynomial Jump-Diffusion Models

TL;DR

This paper introduces a broad mathematical framework for polynomial jump-diffusions, extending affine models, and provides a new method for option pricing and financial asset modeling using these processes.

Contribution

It develops a comprehensive theory for polynomial jump-diffusions, including their transformations and applications in finance, notably in option pricing and asset return modeling.

Findings

Polynomial jump-diffusions preserve their structure under transformations.

A generic method for option pricing using moment expansions is proposed.

New financial asset pricing models with Le9vy-based returns are introduced.

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 L\'evy 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 L\'evy based on polynomial jump-diffusions.