20 lines
1.2 KiB
Markdown
20 lines
1.2 KiB
Markdown
Current Progress Summary:
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The Baseline: We fixed a standard Longstaff-Schwartz (LSM) American Put pricer, correcting the cash-flow propagation logic and regression targets.
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The Evolution: We moved to Bermudan Swaptions using the Hull-White One-Factor Model.
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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.
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The Current Frontier: We were debating the Risk-Neutral Measure (Q) vs. the Terminal Forward Measure (QT).
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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)).
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Pending Topics:
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Mathematical Proof: The derivation of the "Drift Shift" via Girsanov’s Theorem.
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Exercise Boundary Impact: How the choice of measure (and the resulting drift) visually shifts the optimal exercise boundary in simulation.
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Beyond One-Factor: Potential move toward Two-Factor models or non-flat initial term structures.
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