BermudanLsm

Least-squares Monte-Carlo pricing of a Bermudan option by policy optimisation: the continuation value at each exercise date is a low-degree polynomial in log-moneyness whose coefficients beta are chosen to maximise the price under the smoothed exercise rule. The optimised price is a valid lower bound (a sub-optimal policy can only lose value), and at the optimum d(price)/d(beta) = 0, so by the envelope theorem the market Greeks read off the same tape with beta held fixed are correct to first order.

This fills in BermudanOption's Phase-3 hook without an engine "probe replay": the whole valuation stays on one recorded tape, and the coefficient gradient comes from MultiOutput (one forward sweep, one reverse sweep per output) exactly like every other adjoint calibration.