Markov cubature rules for polynomial processes

Damir Filipović (1) , Martin Larsson (2) , Sergio Pulido (3, 4)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 D-MATH - Department of Mathematics [ETH Zurich]
3 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
4 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

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.

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

Domaines: Probabilités [math.PR]

Damir Filipović, Martin Larsson, Sergio Pulido. Markov cubature rules for polynomial processes. Stochastic Processes and their Applications, 2020, 130 (4), pp.1947-1971. ⟨10.1016/j.spa.2019.06.010⟩. ⟨hal-01418755v2⟩