Matlab’s Econometrics Toolbox distinction between Monte Carlo Simulation Trials and Interchangeable Paths
From Matlab’s help system as usual:
Trials vs. Paths
Monte Carlo simulation literature often uses different terminology for the evolution of the simulated variables of interest, such as trials and paths. The following sections use the terms trial and path interchangeably.
However, there are situations where you should distinguish between these terms. Specifically, the term trial often implies the result of an independent random experiment (for example, the evolution of the price of a single stock or portfolio of stocks). Such an experiment computes the average or expected value of a variable of interest (for example, the price of a derivative security) and its associated confidence interval.
By contrast, the term path implies the result of a random experiment that is different or unique from other results, but that may or may not be independent.
The distinction between these terms is usually unimportant. It may, however, be useful when applied to variance reduction techniques that attempt to increase the efficiency of Monte Carlo simulation by inducing dependence across sample paths. A classic example involves pairwise dependence induced by antithetic sampling, and applies to more sophisticated variance reduction techniques, such as stratified sampling.
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