(A) survey on variance reduction techniques in financial simulations

Abstract

Beyond the Black-Scholes-Merton Model, there are many stochastic volatility models who want to reflect more realistic phenomena. As a result, financial simulations under the stocahstic volatility model became more and more complicated. The Monte Carlo method is popular in complicated high dimensional financial simulations. To approve the performance of the Monte Carol method, various variance reduction techniques were developed. In this thesis, we mainly deal with two variance reduction techniques known as the control variates method and the importance sampling method. Our main concern is how to optimize related variance reduction techniques with suitable condtions.