Importance Sampling for Estimating Risk Measures in Portfolio Credit Risk Models

This paper is the report of a Master’s Degree project carried out at Royal Institute of Technology and in this paper we mainly apply the estimators and methods derived by P. Glasserman and J. Li (2003, 2005) of importance sampling methods in portfolio credit risk models. By using the exponential twisting method we will be able to compute the probability beyond one certain loss level (P(L>X)). We use the search method and a ‘direct’ method derived by Peter W. Glynn to estimate the Value-at-Risk (VaR) from the probability and Expected Shortfall (ES) in two portfolio credit risk models, and estimate a convex risk measure Shortfall Risk (SR) with the estimator given by J. Dunkel and S. Weber (2007) in the two models as well. We provide numerical simulation to show the good performance of importance sampling comparing with the plain Monte Carlo.