Stochastic Simulation: Variance Reduction Techniques

This lecture covers variance reduction techniques in stochastic simulation, focusing on the general idea and the use of auxiliary random variables to improve the efficiency of Monte Carlo simulations. The instructor explains how to generate replicas of a stochastic model and compute sample averages, emphasizing the goal of reducing variance. Various methods, such as Crude Monte Carlo, are discussed to achieve this goal, along with the concept of negatively correlated variables. The lecture concludes with the application of these techniques in estimating option prices and modeling asset prices using stochastic processes.