A regular Monte Carlo (MC) simulation algorithm assigns each simulation scenario, or path, an identical probability weight. A weighted Monte Carlo (WMC), however, allows a different probability to be assigned to each simulation path. For example, we can choose the probabilities of each path in a manner such that the simulation is guaranteed to reproduce the prices of “benchmark” securities, whose prices are known from market data. A simulation thus calibrated to benchmarks will then price off-market securities in a realistic manner.

https://ia904705.us.archive.org/20/items/hw-vol/HwVol.pdf