Optimization Of The Importance Sampling For Tail Probability Estimation Of Portfolio Credit Risk

It is a rare event that portfolio credit risk causes significant losses.However,it will cause a serious consequence when it happens.In order to effectively manage the impact of rare events,the primary task is to estimate the probability of rare-events' occurrence,or tail probability.In the calculation,the probability of rare-events' occurrence and the sample size is very small,resulting in large estimation variance.At present,the classical two-step importance sampling algorithm achieves some results in solving this problem.But the classical method uses the zero-variance principle and the maximum principle when constructing the importance distribution function of the risk factor,and this importance distribution function is different from the ideal situation.In this paper,a new importance distribution function is constructed according to the zero-variance principle combined with the central limit theorem.The samples of the risk factor are extracted by the Metropolis-Hastings algorithm,which can effectively reduce the variance of the tail probability estimation.In the aspect of numerical analysis,it is found that the algorithm proposed in this paper can significantly reduce the variance of the tail probability and obtain the expected effect by comparing with the plain Monte Carlo method and the classical two-step importance sampling method.