Markov Cubature Rules for Polynomial Processes
Forthcoming publication in Stochastic Processes and their Applications
31 Pages Posted: 27 Dec 2016 Last revised: 13 Jun 2019
Date Written: June 10, 2019
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: Suggested Citation