Importance Sampling

Importance sampling is a technique used in Monte Carlo simulations to focus computational resources on the most critical regions of a probability distribution. In the context of derivative pricing, this often involves shifting the probability measure so that rare, high-impact events ⎊ such as deep out-of-the-money option exercises ⎊ occur more frequently during the simulation.

By weighting the resulting outcomes appropriately to account for this change in distribution, the simulation produces a more accurate estimate of the expected value. This is especially useful for calculating the risk of extreme tail events or pricing options with complex payout structures where standard sampling might miss important market dynamics.

It effectively reduces the variance of the estimator by ensuring that the simulation explores the relevant scenarios that drive the derivative's value.