[QL-9.x][DEFER] MC remainder: Brownian bridge, control variates and TimeGrid accessor #453

Audited 2026-09-27 against released v0.29.0. Deferred remainder, under #71. The original MultiPath/LSM/Sobol backlog is mostly delivered; do not reimplement those components.

Delivered

• MultiPath and MultiPathGenerator ([QL-9.x] MultiPath + MultiPathGenerator, multi-factor path generation (Batch HMC 2/4) #476), generalized Monte Carlo accumulation and antithetic averaging ([QL-9.x] Generalize the Monte-Carlo stack over path type + antithetic averaging (Batch HMC 3/4) #477), and the European Heston consumer/shared engine base ([QL-11.x] MCEuropeanHestonEngine + testMcVsCached bit-exact cached gate (Batch HMC 4/4) #478/[QL-11.x] Unify McVanillaEngineBase on the multi-factor StochasticProcess #482).
• Scalar antithetic generation and single-asset Longstaff-Schwartz American/Bermudan pricing ([MC-American][T2] EarlyExercisePathPricer trait + LsmBasisSystem + PathPricer-for-Shared bridge #759-[MC-American][T4] MCLongstaffSchwartzEngine + MCAmericanEngine + MakeMCAmericanEngine #761, [MC-American][DEFER] Depth: remaining testAmericanOption grid + Gauss basis families + BermudanExercise #763).
• LowDiscrepancy/Sobol European engine policy ([QL-9.x][DEFER] Low-discrepancy RSG bundle + scalar InverseCumulativeRng + Poisson traits #454), with fixed-sample semantics rather than unsupported QMC error estimates.
• Mandatory-time TimeGrid constructors, index and closest_index are present in TimeGrid.

Remaining

• Implement scalar BrownianBridge and the bridge-enabled PathGenerator path. The released PathGenerator explicitly rejects it.
• Add control-variate accumulation and simulation/engine plumbing. Released McSimulation still rejects control_variate=true.
• Add the original TimeGrid::closest_time convenience accessor, which is still absent; preserve existing index/closest_index behavior.

Activation and acceptance

Activate with a named scalar pricing consumer and a bounded bridge or control-variate slice. Verify bridge endpoint/distribution behavior on nonuniform time grids, deterministic draw ordering, forward/antithetic reuse, estimator weighting and a reference control-variate price. Preserve all existing seeded MC and Heston regressions without widening tolerances. Pair newly exposed pricing controls with Python/C/Go tests and document unsupported combinations.

MultiPath bridge remains explicitly unsupported in both this port and the referenced QuantLib generator; any implementation needs a separately agreed extension contract rather than an assumed parity requirement. Multi-asset LSM and Sobol LSM are outside this refreshed original remainder. Keep this ticket open until the checklist is delivered or its scope is explicitly superseded.