feat(american-option): log-spot Dynamic Chebyshev variant (Stage F1 front-fixing)#228
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…ront-fixing) Add a default-off LogSpot build option that interpolates the continuation in x = log(S) instead of linear S. The GBM transition is additive in x, so the Gauss-Hermite images stay bounded, and the narrow uniform-in-x grid is far better conditioned than the wide linear [5,250] grid at high node counts. Two measured wins vs the linear grid (StandardPut, oracle Gamma(82)=0.033689): (1) Robustness - log-spot stays finite at n=321 where the linear build throws 'function returned non-finite values', and at n=161 the linear spot-82 row wrongly collapses into the exercise region (Gamma 0) while log-spot gives 0.027767. (2) Accuracy - the spot-82 Gamma error converges monotonically with n (0.009807 -> 0.005922 -> 0.002755), more than halving it, so the boundary Gamma error was resolution-limited, not intrinsic. At low n=81 log-spot is marginally behind linear near the boundary, where its nodes cluster at the domain ends. Greeks use the chain rule from u(x)=V(e^x): Delta = u'(x)/S, Gamma = (u''-u')/S^2 (the -u' term is required). The OFF path is bit-identical (additive branch; existing linear code verbatim in the else arm). This recovers most of the boundary Gamma without the heavyweight boundary-tracking (Landau) re-architecture, now optional. Docs: case-study subsection 'A log-spot variant recovers the boundary Gamma'. Tests: OFF bit-identical lock; log-spot ATM price vs oracle; chain-rule Greeks vs linear baseline; finite-at-high-n where linear throws; spot-82 Gamma convergence measurement. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…the boundary finder Now that the log-spot variant is the real boundary-aware path, retire the naive BoundarySplit flag. It splits a smooth continuation at a non-singularity and only relocates the Gamma query onto the ill-conditioned Chebyshev piece edge (non-physical negative Gamma). The documented finding stays in the case study; the reusable FindExerciseBoundary (Math.NET Brent) is kept. Removed: the BoundarySplit settings flag, the split branch in Build, BuildContinuationSpline, EvaluateSpline, the now-unused firstContinuationFunction/firstFunc plumbing, and the two split-specific tests. Kept: FindExerciseBoundary + its test (renamed AmericanOptionBoundaryFinderTests). Docs: added the concrete global-vs-split Gamma-ringing table to the negative-result note (preserving the evidence now that the runnable flag is gone), and fixed the high-n failure description (ill-conditioning of the wide grid, not quadrature overflow). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Summary
Stacked on #227 (base =
feature/american-boundary-split). Stage F1 of the front-fixing track: a default-offLogSpotbuild option that interpolates the continuation inx = log(S)instead of linearS— and it retires the naiveBoundarySplitexperiment from #227 now that log-spot supersedes it.This answers the open question from #227's negative result: the boundary Gamma error was resolution-limited, not intrinsic.
Why log-spot
The GBM transition
S' = S·exp(drift + √2·σ√dt·z)becomes additive inx = log(S):x' = x + drift + √2·σ√dt·z. So the Gauss–Hermite images stay bounded, and the grid is narrow ([log5, log250], ~24× tighter span) and uniform-in-x, hence far better conditioned than the wide linear[5,250]grid.Measured (StandardPut, oracle Γ(82) = 0.033689)
nn=321where the linear build throws "function returned non-finite values".n=81log-spot trails linear near the boundary, where its Type-I nodes cluster at the domain ends.This makes the heavyweight F2 (boundary-tracked Landau transform) optional.
Also retires the
BoundarySplitexperiment (from #227)Now that log-spot is the real boundary-aware path, this PR retires the naive
BoundarySplitflag — it split a smooth continuation at a non-singularity and only relocated the Gamma query onto the ill-conditioned piece edge (non-physical negative Gamma).BuildContinuationSpline/EvaluateSpline, dead plumbing, and the two split tests.FindExerciseBoundary(Brent, reusable) + its test (renamedAmericanOptionBoundaryFinderTests).Net: published
main(after the stack merges) gets the log-spot fix and the documented lesson, not the broken flag.Implementation
LogSpotflag (default off); the OFF path is bit-identical (additive branch — regression-locked).u(x) = V(e^x):Δ = u'(x)/S,Γ = (u''(x) − u'(x))/S²(the−u'term is required).Tests / gates
OFF bit-identical lock; log-spot ATM price vs oracle; chain-rule Greeks vs linear baseline; finite-at-high-
nwhere linear throws; spot-82 Gamma convergence measurement; boundary-finder test. Full suite 1804 passed,dotnet formatclean,docfx0/0.Sequencing
Stacked on #227. Merge order: #226 → #227 → this. GitHub retargets this to
mainonce #227 merges.🤖 Generated with Claude Code