Variance reduction for multivariate Monte Carlo simulation

In practice, the rate of convergence for Monte Carlo simulation is often unsatisfactory when a large number of underlying variables arc involved. The reason behind this deficiency is the mismatch between the prespecified and the sample variance-covariance matrices of the underlying multivariate random samples, upon which the value of the option of interest is highly dependent. In this article, a new method, termed the inverse Cholesky decomposition transformation, is proposed to rectify this problem, in which crude independent standard normal distributed random samples are viewed as weakly correlated, normally distributed random samples transformed from truly independent standard normal distributed random samples via the Cholesky decomposition tran formation. In simulation of European calls on the maximum of 10 assets, the proposed method achieves a root mean squared error (RMSE:) about one-third of that of the standard Monte Carlo simulation under the same number of simulations. Furthermore, the analysis of the RMSE and the computational time demonstrates this new method superior efficiency compared with the traditional variance-reduction techniques. Accordingly, the proposed method is suggested as one of the standard procedures in multivariate Monte Carlo simulation.