New Approaches to Importance Sampling for Portfolio Credit Risk Valuation by Zhe Wang

New Approaches to Importance Sampling for Portfolio Credit Risk Valuation Zhe Wang Master of Science Graduate Department of Computer Science University of Toronto 2015 Portfolio credit risk based on the Gaussian Copula model has been widely studied and generally evaluated through Monte Carlo simulations. The two-level structure, namely systematic factors and individual factors, complicates the problem in a way that traditional variance reduction techniques become very hard to apply. Glasserman and Li proposed a two-level importance sampling approach to tackle a simplified binary credit states problem. The inner level was approximated through a conditional importance sampling approach using an exponential twisting technique. In this research project, we propose an alternative importance sampling approach which uses the Central Limit Theorem for the inner level. Our approach can be easily generalized to multi-credit states. Based on this approximation, we then propose two novel approaches motivated from research in machine learning. Instead of finding the importance sampler through an optimization problem, the first approach approximates the zero variance function by learning from the samples which are generated from Markov Chain Monte Carlo. The second approach treats the problem as a Bayesian inference problem and evaluates the tail probability through Bayesian Monte Carlo. Compared to Glasserman and Li’s method, numerical results show that these two new approaches have advantages in both accuracy and speed and are also more easily adapted to other applications.