  Corporate defaults may be triggered by some major market news or events such
as financial crises or collapses of major banks or financial institutions. With
a view to develop a more realistic model for credit risk analysis, we introduce
a new type of reduced-form intensity-based model that can incorporate the
impacts of both observable "trigger" events and economic environment on
corporate defaults. The key idea of the model is to augment a Cox process with
trigger events. Both single-default and multiple-default cases are considered
in this paper. In the former case, a simple expression for the distribution of
the default time is obtained. Applications of the proposed model to price
defaultable bonds and multi-name Credit Default Swaps (CDSs) are provided.
