wegamekinglc / Derivatives-Algorithms-Lib / 36300816446

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feat: add multi-state LSM for multi-asset MC pricing (#449)

* Add multistate LSM for multi-asset Monte Carlo pricing

Allow exercise products to select named equity outputs and scalar script states so hybrid and correlated-equity continuation policies can depend on the full payoff state. Fit bounded standardized cross-term bases with rank-aware QR and optional held-out degree selection, then reuse the frozen policy in hard and AAD replay. Preserve scalar defaults and older product archives while exposing the selection across C++, Python, and Excel.

* Preserve scalar regressor identity in LSM diagnostics

Explicit single-equity state selection should retain the existing regressor_index join key in diagnostics. Multi-state and script-variable selections continue to report their names in regression_features.

* Simplify multistate QR and preserve fallback diagnostics

Split the QR and feature-resolution steps into small focused helpers so the new fit remains straightforward to audit. Report zero rank when no paths enter regression, retain the constant-fit fallback reason, and cover multifactored Brownian bridge pricing.

* test: initialize Excel runtime for hybrid tests on Windows

The Windows XLL and test executable have separate statically linked DAL state. Initialize both before parsing named equity indices and set the XLL evaluation date for the multi-state Bermudan coverage.

* test: demonstrate value of two-state Bermudan regression

Compare frozen two-equity Bermudan payoffs against an independent exchange-option reference. The paired one-state policy shows the price lost when a relevant script variable is omitted; surface that comparison in the C++ and Python examples and LSM guide.

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