Simulation for American Options: Regression Now or Regression Later?

Pricing American options requires solving an optimal stopping problem and therefore presents a challenge for simulation. This article investigates connections between a weighted Monte Carlo technique and regression-based methods for this problem. The weighted Monte Carlo technique is shown to be equivalent to a least-squares method in which option values are regressed at a later time than in other regression-based methods. This "regression later" technique is shown to have two attractive features: under appropriate conditions, (i) it results in less-dispersed estimates, and (ii) it provides a dual estimate (an upper bound) with modest additional effort. These features result, more generally, from using martingale regressors.