Importance Sampling for Estimating High Dimensional Joint Default Probabilities

• Main Authors: Yen-An Chen, 陳彥安
• Other Authors: 韓傳祥
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/hfqq5e

碩士 === 國立臺灣大學 === 應用數學科學研究所 === 105 === We discuss the simulation method for estimating the probabilities of rare events, especially the “joint default” probabilities under different models. The methods we provide are based on importance sampling, which is a variance re- duction technique used to increase the number of samples reaching the “rare” region. There are two parts in this thesis. For the first part, we provide several importance sampling schemes, where the “asymptotically optimal” (or efficient) property is proved by applying the large deviation theory. Also, the results could be applied to the multi-dimensional scene, where most of the probabilities interested do not have an explicit expression. For the second part, we apply our idea to the model that is more complicated. It is shown that we have some satisfying results while keeping the computation efficient.