Markov Cubature Rules for Polynomial Processes

Forthcoming publication in Stochastic Processes and their Applications

Swiss Finance Institute Research Paper No. 16-79

31 Pages Posted: 27 Dec 2016 Last revised: 13 Jun 2019

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

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: June 10, 2019

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 such rules using algebraic techniques. Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial processes.

Keywords: Polynomial process; cubature rule; asymptotic moments; transition rate matrix; transition probabilities; American options

JEL Classification: C63, G12, G13

Suggested Citation

Filipovic, Damir and Larsson, Martin and Pulido, Sergio, Markov Cubature Rules for Polynomial Processes (June 10, 2019). Forthcoming publication in Stochastic Processes and their Applications; Swiss Finance Institute Research Paper No. 16-79. Available at SSRN: https://ssrn.com/abstract=2890002 or http://dx.doi.org/10.2139/ssrn.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

Swiss Finance Institute

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