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[QL-9.x][DEFER] FDM remainder: sparse operators, Krylov, boundaries and multidimensional engines #636

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[QL-9.x][DEFER] FDM remainder: sparse operators, Krylov, boundaries and multidimensional engines#636
Milestone
EPIC-9: Methods (L9)

Description

@benbenbang
benbenbang
opened on Jul 28, 2026

Audited 2026-09-27 against released v0.29.0. Deferred framework remainder, under #71. The baseline now includes European, American and Bermudan Black-Scholes FD pricing; the old European-only description is obsolete.

Delivered

The FD implementation includes meshes, tridiagonal operators, step/boundary abstractions, Douglas and 1-D implicit-Euler rollback, solver wrappers and Greeks (#635). American and Bermudan exercise conditions shipped in #826/#827. The engine is available through Python/C/Go (#1108/#1109). These are not outstanding framework tasks.

Remaining

  • Matrix export (toMatrix/toMatrixDecomp), sparse-matrix representation and NumericalDifferentiation/nonuniform derivative-weight coverage. The released FdmLinearOp trait still omits matrix export.
  • BiCGstab/GMRES and the multidirectional implicit-Euler branch; ImplicitEulerScheme rejects that branch today.
  • Concrete Dirichlet/Neumann boundaries and a pricing consumer using a nonempty boundary set. Generic boundary hooks are already present.
  • Actual multidimensional mixed/directional operators and splitting consumers beyond 1-D Black-Scholes.
  • Non-Black-Scholes FD operators/engines, including Heston, CEV, CIR, Bates and SABR, activated in individually scoped increments.
  • MakeFdBlackScholesVanillaEngine builder/remaining constructor surface.
  • [QL-9.x][FDM][DEFER] FD vanilla engine dividend/escrowed/quanto/local-vol paths #828: cash-dividend, escrowed, quanto and local-vol vanilla paths; that issue owns their detailed checklist.

Activation and acceptance

Remain deferred until a concrete downstream engine requires each capability. Start from that consumer's dependencies; do not port the full framework speculatively. Each increment needs matrix/operator or solver reference tests plus an end-to-end numerical oracle. Existing FD prices, Greeks, early-exercise conditions and platform-specific regression tolerances must remain unchanged. Pair new public pricing surfaces with Python/C/Go bindings, and document Rust-only generic machinery explicitly. Close only when the remaining scope is completed or explicitly superseded by agreed trackers.

Activity

  1. benbenbang
    added this to the EPIC-9: Methods (L9) milestone on Jul 28, 2026

  2. benbenbang commented on Jul 28, 2026

    @benbenbang
    benbenbang
    on Jul 28, 2026
    MemberAuthor

    Batch-2 deferrals recorded (all verified unreached by any batch-2 oracle, gate-confirmed):

  3. benbenbang commented on Jul 28, 2026

    @benbenbang
    benbenbang
    on Jul 28, 2026
    MemberAuthor

    Two more calculator deferrals from B2-T3 (#647), documented in the module doc of utilities/fdminnervaluecalculator.rs:

    • FdmZeroInnerValue (fdminnervaluecalculator.hpp:93) - trivial (~4 lines); only consumers are the swing/VPP engines (fdsimplebsswingengine.cpp:69 + experimental). Pull forward whenever a consumer lands.
    • FdmLogBasketInnerValue (hpp:80) - needs the unported BasketPayoff; only consumer fd2dblackscholesvanillaengine.cpp:76, so it belongs with the basket work.

    Also noting from B2-T2 (#646) for the batch-3 oracle ticket: the mesher's 24.0*maturity intermediate-step constant is source-verified but UNPINNED by any test (both mesher fixtures are monotone between dividends, so the intermediate samples never bind on mi/ma; a mutation to 0.1 stays green). The batch-3/4 oracles do not discriminate it either - do not let a green suite justify simplifying that loop.

  4. benbenbang commented on Jul 30, 2026

    @benbenbang
    benbenbang
    on Jul 30, 2026
    MemberAuthor

    Batch-4 (final) deferrals - the European Black-Scholes FD vertical closes with batch 4 (#665-669); everything below is explicitly OUT of the epic, verified unreached by testFdEngines/testFdEngineWithNonConstantParameters (gate-confirmed):

    • 7 FDM schemes: CrankNicolson, ExplicitEuler, MethodOfLines, Hundsdorfer, CraigSneyd, ModifiedCraigSneyd, TrBDF2 - their FdmSchemeDesc factories AND FdmBackwardSolver dispatch arms (currently a typed Err citing this issue).
    • testPDESchemes (full 9-scheme, europeanoption.cpp:1479), testLocalVolatility (:1295), testDouglasVsCrankNicolson (:1633).
    • Dividends / early exercise: Spot + Escrowed cash-dividend models, EscrowedDividendAdjustment, FdmEscrowedLogInnerValueCalculator, FdmDividendHandler, FdmAmericanStepCondition, FdmBermudanStepCondition, full FdmStepConditionComposite::vanillaComposite.
    • Quanto (FdmQuantoHelper), local-vol engine path, MakeFdBlackScholesVanillaEngine fluent builder + the 3 extra engine ctors.
    • 2-D solvers (FdmHestonSolver + the fdmlinearop.cpp Heston createSolverDesc path).
      These unblock later FD engines (American/barrier/local-vol/Heston-FD) - none needed for the European vanilla vertical.
  5. cursor
    added a commit that references this issue on Aug 2, 2026

    feat(exercise): American/Bermudan exercise and FD American engine

    cc86a2a

  6. benbenbang commented on Aug 9, 2026

    @benbenbang
    benbenbang
    on Aug 9, 2026
    MemberAuthor

    Batch FDM-A record (orchestrator): COMPLETE, awaiting merge. Stack: main <- fable/826 (8a05369, American FD: FdmAmericanStepCondition + vanilla_composite + engine wiring + Ju/window oracles) <- fable/827 (da44225, Bermudan FD: BermudanExercise + FdmBermudanStepCondition + 3-arm degeneracy oracle). Both gated PASS; suite 2496 -> 2515; all probes bit, incl. the European-aliasing trap caught by the 9.065 Ju row and the no-op-condition trap caught by the strict-above-European arm. Deferral #828 (dividends/Escrowed/quanto/localVol) on the board; the rest of #636 (toMatrix/Krylov/N-D/non-BS) unchanged.

  7. cursor
    added a commit that references this issue on Aug 23, 2026

    fix(equity): drop 2-D implicit-Euler damping on Heston quanto

    dd079c8
  8. zhangys2
    added a commit that references this issue on Aug 24, 2026

    feat(equity): Heston FD quanto and American vanilla engine (#85)

    226dc3a
  9. zhangys2
    added 2 commits that reference this issue on Sep 19, 2026

    test(equity): fdheston.cpp FD scheme and American/barrier NPV oracles

    ce74649

    test(equity): drop FdHeston CN arm until 2-D ImplicitEuler

    2d3a254
  10. benbenbang
    changed the title [-][QL-9.x][EPIC-9][DEFER] FDM machinery beyond the European BS vertical (toMatrix/SparseMatrix, Krylov, boundaries, N-D, non-BS ops)[/-] [+][QL-9.x][DEFER] FDM remainder: sparse operators, Krylov, boundaries and multidimensional engines[/+] on Sep 27, 2026
  11. benbenbang
    added a parent issue on Oct 30, 2026
  12. benbenbang
    added a commit that references this issue on Nov 8, 2026

    feat(fdm): wire Spot cash-dividend model into FdBlackScholesVanillaEn…

    9c4746b
  13. ptah-bw-technical-app
    added a commit that references this issue on Nov 8, 2026

    chore(release): update version to 0.49.0 [skip ci]

    3f76949
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