Abstract
The loss density function is useful for pricing credit derivatives and risk management of credit portfolio. The loss density function concludes estimating the joint default probability and survival probability. Under the structural-form model, computation of the loss density function relies on the estimates of some mixture of joint default probability and joint survival probability. We provide several efficient importance sampling methods to estimate the probability of defaultable and/or survival event. We also provide an empirical study of a correlated hedging for CDS spread.