1.2 KiB
1.2 KiB
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 ∫rsds. 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.