A Structural Jump Threshold Framework for Credit Risk

This paper presents a new structural framework for multidimensional default risk. We define the time of default as the first time the log-return of the stock price of a firm jumps below a (possibly nonconstant) default level. When stock prices are exponential Lévy, this framework is equivalent to a reduced form approach, where the intensity process is parametrized by a Lévy measure. The dependence between the default times of firms within a basket of credit securities is the result of the jump dependence of their respective stock prices, making the link between the equity and credit markets. We value a first-to-default basket credit default swap (CDS) as an application.