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Markov Cubature Rules for Polynomial Processes

30 Pages Posted: 27 Dec 2016 Last revised: 22 Jul 2017

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Ecole Polytechnique Fédérale de Lausanne

Martin Larsson

ETH Zurich - Department of Mathematics

Sergio Pulido

Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, Université Paris-Saclay, UMR CNRS 8071

Date Written: July 21, 2017

Abstract

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractability and ease the implementation of models where the underlying factors are polynomial processes.

Keywords: Polynomial Process, Cubature Rule, Asymptotic Moments, Transition Rate Matrix, Transition Probabilities, Negative Probabilities

JEL Classification: C63, C65

Suggested Citation

Filipović, Damir and Larsson, Martin and Pulido, Sergio, Markov Cubature Rules for Polynomial Processes (July 21, 2017). Swiss Finance Institute Research Paper No. 16-79. Available at SSRN: https://ssrn.com/abstract=2890002

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

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

Ecole Polytechnique Fédérale de Lausanne - Ecole Polytechnique Fédérale de Lausanne ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland

Martin Larsson

ETH Zurich - Department of Mathematics ( email )

Ramistrasse 101
Zurich, 8092
Switzerland

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

Sergio Pulido

Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, Université Paris-Saclay, UMR CNRS 8071 ( email )

IBGBI 23 Boulevard de France
Évry Cedex, 91037
France

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