Polynomial Jump-Diffusion Models

40 Pages Posted: 27 Nov 2017 Last revised: 22 Jul 2019

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Martin Larsson

ETH Zürich - Department of Mathematics

Date Written: January 2, 2019

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.

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

Filipovic, Damir and Larsson, Martin, Polynomial Jump-Diffusion Models (January 2, 2019). Swiss Finance Institute Research Paper No. 17-60. Available at SSRN: https://ssrn.com/abstract=3075520 or http://dx.doi.org/10.2139/ssrn.3075520

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Martin Larsson

ETH Zürich - Department of Mathematics ( email )

Ramistrasse 101
Zurich, 8092
Switzerland

HOME PAGE: http://math.ethz.ch/~larssonm

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