Least-squares Monte Carlo (Longstaff-Schwartz)
Quantitative Finance glossary · Numerical Methods & Optimization
Definition
Monte Carlo algorithm for pricing American/Bermudan options. At each exercise date, regress the discounted continuation value on basis functions of the state (1, S, S^2, ldots or Laguerre polynomials) across paths, then exercise when immediate payoff exceeds the fitted continuation value. Bridges the dimension wall of PDE methods (which scale exponentially with factors) — LSM scales linearly, making it the standard for high-dimensional Bermudans (callable structured notes, autocallables).
Least-squares Monte Carlo (Longstaff-Schwartz) in plain English
Some options let you cash out *early*, any time you like, which makes them hard to price: at every moment you must decide "grab the payoff now, or wait for possibly more?" Least-squares Monte Carlo answers this by simulating thousands of random price paths into the future, then, at each decision date, using a quick best-fit curve (a regression) to *estimate* the average payoff of waiting. You then compare: if cashing out now beats that estimated "keep waiting" value, you exercise. Its superpower is scaling: older grid-based methods choke when an option depends on many moving pieces (their work explodes), while this approach stays manageable — making it the go-to for complex modern products like autocallables and callable notes.
Also called: Longstaff-Schwartz
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