Markov Cubature Rules for Polynomial Processes

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