Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula

Abstract

This paper proposes an efficient simulation method for calculating credit portfolio risk when risk factors have a heavy-tailed distributions. In modeling heavy tails, its features of return on underlying asset are captured by multivariate [Formula: see text]-Copula. Moreover, we develop a three-step importance sampling (IS) procedure in the [Formula: see text]-copula credit portfolio risk measure model for further variance reduction. Simultaneously, we apply the Levenberg–Marquardt algorithm associated with nonlinear optimization technique to solve the problem that estimates the mean-shift vector of the systematic risk factors after the probability measure change. Numerical results show that those methods developed in the [Formula: see text]-copula model can produce large variance reduction relative to the plain Monte Carlo method, to estimate more accurately tail probability of credit portfolio loss distribution.