Abstract
We propose a systematic procedure to implement an importance sampling method for efficiently computing the probability of high-dimensional rare events based on a copula framework. The tilted distribution is optimal in the sense that the asymptotic variance is minimized. Our method includes the following steps. First, we transform the variables to uniform random variables. Second, we change a measure on the uniform random variables and use recursive method to find the optimal tilting measure. Finally, we have an efficient estimation using the optimal measure on the transformed random variables. We illustrate our approach through several popular copula models.