Stopping simulated paths early

We provide results about stopping simulation paths early as a variance reduction technique, adding to our earlier work on this topic. The problem of pricing a financial instrument with cashflows at multiple times, such as a mortgage-backed security, motivates this approach, which is more broadly applicable to problems in which early steps are more informative than later steps of a path. We prove a limit theorem that demonstrates that this relative informativeness of simulation steps, not the number of steps, determines the effectiveness of the method. Next we consider an extension of the idea of stopping simulation paths early, showing how early stopping can be random and depend on the state a path has reached, yet still produce an unbiased estimator. We illustrate the potential effectiveness of such estimators, and describe directions for future research into their design.