wegamekinglc / Derivatives-Algorithms-Lib / 35464753232

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DAL-281: tree-walk LSMC core and Bermudan PDE benchmark (T2) (#398)

* Add tree-walk LSMC valuation for EXERCISE products (T2)

Three-phase double-mode driver behind MCDoubleSimulation routing: forward
storage of raw payments and (x, h, condition) triples over the fixed
min(8192, nPaths) batch layout, single-threaded backward induction with
z-normalized monomial continuation regressions (sigma floor, explicit
relative ridge, sample-size and conditioning guards with constant-basis
degenerate paths), and a frozen-strategy sobol replay whose batch-index
reductions keep PV, coefficients and exercise rates bitwise invariant to
the thread count. Adds the dal.script-simulation/1 diagnostic
(ExplainScriptSimulation in core and dal-public) and a test-only
Bermudan PDE benchmark anchoring the acceptance suite.

Co-authored-by: multica-agent <github@multica.ai>

* Split the three high-complexity LSMC functions under the Codacy gate

SolveExerciseRegression (17), RunBackwardPhase (13) and
ExplainScriptSimulation (10) exceeded the complexity-8 standard; extract
the regression statistics/normal-equations/ridge helpers, the backward
induction and decision helpers, and the diagnostic run/serialization
helpers. The arithmetic and statement order are untouched, so the bitwise
invariance and zero-exercise acceptance tests confirm behavior identity.

Co-authored-by: multica-agent <github@multica.ai>

* Fix the Copilot review findings on the LSMC payoff and diagnostics

- Keep the PAYS cashflows accumulated strictly before the exercise date in
  the exercised path payoff: exercise replaces same-day and later payments
  only (S4), so a coupon before the first exercise survives it; the
  recording evaluator snapshots the payoff variable at the exercise-event
  boundary and the replay adds it to the discounted exercise value, with a
  deterministic-economy regression case locking the composition
- Reject a negative numPath in ExplainScriptSimulation before the size_t
  conve... (continued)

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