Markov cubature rules for polynomial processes

TL;DR

This paper introduces Markov cubature rules for polynomial processes, enabling efficient discretization and improved tractability of complex path-dependent financial tasks like American option pricing.

Contribution

It develops a novel algebraic framework for constructing Markov cubature rules that match moments of polynomial processes, enhancing computational methods in finance.

Findings

Markov cubature rules effectively approximate polynomial processes.

The approach simplifies pricing of American options in polynomial models.

Algebraic techniques facilitate the construction of these rules.

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.