Low-rank kernel methods for American option pricing
This work addresses the computational bottleneck of recursive Monte Carlo optimal stopping for practitioners in quantitative finance, offering a more efficient and theoretically grounded alternative.
We propose a low-rank kernel method for American option pricing that reformulates continuation value estimation as a learning problem in a reproducing kernel Hilbert space, achieving an offline-online decomposition that eliminates recomputation across exercise dates. Numerical experiments demonstrate speed and accuracy improvements over existing methods.
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.