  This article presents a simple but effective and efficient approach to
improve the accuracy and stability of Least-Squares Monte Carlo for
American-style option pricing as well as expected exposure calculation in
valuation adjustments. The key idea is to construct the ansatz of conditional
expected continuation payoff using the exact solution from low dimensional
finite difference methods, to be used in linear regression. This approach
bridges between solving backward partial differential equations and Monte Carlo
simulation, aiming at achieving the best of both worlds. We illustrate the
technique with realistic examples including Bermudan options, worst of issuer
callable notes and expected positive exposure on European options. The method
can be considered as a generic numerical scheme across various asset classes,
in particular, as an accurate method for pricing and risk-managing
American-style derivatives under arbitrary dimensions.

General Finance;Computational Finance