Current Progress Summary:

    The Baseline: We fixed a standard Longstaff-Schwartz (LSM) American Put pricer, correcting the cash-flow propagation logic and regression targets.

    The Evolution: We moved to Bermudan Swaptions using the Hull-White One-Factor Model.

    The "Gold Standard": We implemented a 100% exact simulation from scratch. Instead of Euler discretization, we used Bivariate Normal sampling to jointly simulate the short rate rt​ and the stochastic integral ∫rs​ds. This accounts for the stochastic discount factor (the convexity adjustment) without approximation error.

    The Current Frontier: We were debating the Risk-Neutral Measure (Q) vs. the Terminal Forward Measure (QT).

        We concluded that while QT simplifies European options, it makes Bermudan LSM "messy" because it introduces a time-dependent drift shift: DriftQT​=DriftQ​−aσ2​(1−e−a(T−t)).

Pending Topics:

    Mathematical Proof: The derivation of the "Drift Shift" via Girsanov’s Theorem.

    Exercise Boundary Impact: How the choice of measure (and the resulting drift) visually shifts the optimal exercise boundary in simulation.

    Beyond One-Factor: Potential move toward Two-Factor models or non-flat initial term structures.