In this paper, we establish a class of default risk models with possible dynamical contagion between different obligors. Thereby, we derive explicitly the pricing formulae by set-valued Markov chain approach. As an application, we employ the default contagion model to price synthetic CDOs. The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ }  .
In this paper, we establish a new default risk framework with possible dynamical contagion among obligors. Thereby, we derive analytically the dynamics of the default process by set-valued Markov chain approach. Applying the new framework, we give analytical pricing formulaes for synthetic collateralized debt obligations (CDOs). The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das, Duffie, Kapadia and Saita The Journal of Finance, 2007]{DasDuffie2007 and Duffie, Eckner, Horel and Saita[The Journal of Finance, 2009 duffieEHS2009} demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
R
class of default risk models
new default risk framework
R
between different
among
R
explicitly the pricing formulae
analytically the dynamics of the default process
R
As an application, we employ the default contagion model to price synthetic CDOs. The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large
Applying the new framework, we give analytical pricing formulaes for synthetic collateralized debt obligations (CDOs). The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das, Duffie, Kapadia and Saita
A
The Journal of Finance, 2007
A
DasDuffie2007
A
and Duffie, Eckner, Horel and Saita
A
The Journal of Finance, 2009
A
duffieEHS2009
A
demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms)