Low-rank kernel methods for American option pricing

TL;DR

This paper introduces a low-rank kernel-based method for American option pricing that improves computational efficiency and accuracy by learning a single operator offline, then applying it across all exercise dates.

Contribution

The paper presents a novel low-rank kernel approach that reformulates continuation value estimation as a learning problem, enabling scalable and theoretically justified American option pricing.

Findings

Method achieves faster computation compared to existing techniques.

The approach provides strong convergence guarantees.

Numerical results show high accuracy in option pricing.

Abstract

We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation values as a learning problem in a reproducing kernel Hilbert space, in which the conditional expectation is represented as a linear operator acting on future payoffs. This perspective yields an offline-online decomposition: the operator is learned once from simulated data and subsequently reused across all exercise dates, eliminating the need to recompute regression models at each step of the backward recursion. We establish convergence guarantees and derive bounds quantifying the approximation errors across exercise dates. Numerical experiments demonstrate the speed and accuracy of the proposed approach relative to extant methods.