Latin Hypercube Sampling

Latin hypercube sampling is a statistical method for generating a sample of plausible collections of parameter values from a multidimensional distribution. It ensures that each input variable is sampled across its entire range, providing a more uniform coverage of the input space than simple random sampling.

By dividing the range of each variable into equal-probability intervals and ensuring each interval is sampled exactly once, the method forces the simulation to explore all regions of the parameter space. This leads to a more robust estimation of derivative prices and sensitivities, particularly when multiple risk factors are involved.

In financial engineering, this technique helps in capturing the interaction between various market variables more efficiently. It reduces the number of iterations required to achieve a stable result by avoiding the clustering often found in purely random sampling.