Density Approximations for Multivariate Affine Jump-Diffusion Processes

42 Pages Posted: 26 May 2011 Last revised: 17 Mar 2013

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Eberhard Mayerhofer

University of Limerick - Department of Mathematics and Statistics

Paul Schneider

University of Lugano - Institute of Finance; Swiss Finance Institute

Date Written: May 24, 2011

Abstract

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

Keywords: Affine Processes, Asymptotic Expansion, Density Approximation, Orthogonal Polynomials

JEL Classification: G12, C13, C32

Suggested Citation

Filipovic, Damir and Mayerhofer, Eberhard and Schneider, Paul Georg, Density Approximations for Multivariate Affine Jump-Diffusion Processes (May 24, 2011). Swiss Finance Institute Research Paper No. 11-20. Available at SSRN: https://ssrn.com/abstract=1851511 or http://dx.doi.org/10.2139/ssrn.1851511

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

Eberhard Mayerhofer

University of Limerick - Department of Mathematics and Statistics ( email )

Castletroy, Co
Limerick
Ireland

Paul Georg Schneider

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

Swiss Finance Institute ( email )

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

Register to save articles to
your library

Register

Paper statistics

Downloads
611
Abstract Views
3,069
rank
42,882
PlumX Metrics