How Longstaff-Schwartz handles early exercise

Describe the Longstaff-Schwartz method for pricing options with early exercise by simulation.

Estimate continuation values by regression and work backwards along simulated paths. Simulate paths forward; at expiry record the payoff. Stepping back, at each exercise date regress the discounted future cash flows on basis functions of the state, using only in-the-money paths, to estimate the value of continuing. Exercise where intrinsic value beats that estimate and update the path's cash flow. The average discounted cash flow gives a (low-biased) price; an independent set of paths removes foresight bias.