Extreme Value Importance Sampling for Rare Event Risk Measurement [chapter]

D. L. McLeish, Zhongxian Men
2015 Innovations in Quantitative Risk Management  
We suggest practical and simple methods for Monte Carlo estimation of the (small) probabilities of large losses using importance sampling. We argue that a simple optimal choice of importance sampling distribution is a member of the generalized extreme value distribution and, unlike the common alternatives such as Esscher transform, this family achieves bounded relative error in the tail. Examples of simulating rare event probabilities and conditional tail expectations are given and very large efficiency gains are achieved.
doi:10.1007/978-3-319-09114-3_18 fatcat:mydms24ptnddhhf6itp6lvfyfe