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%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% 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) .
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk %DIFDELCMD < ]{%%% %DIFDELCMD < [%%% %DIFDELCMD < } %%% .
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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
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a
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Markov chain approach. Applying the new framework, we give analytical pricing formulaes
Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms
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The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence
Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support
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coupling
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as Das, Duffie, Kapadia and Saita
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The Journal of Finance, 2007
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DasDuffie2007
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and Duffie, Eckner, Horel and Saita
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The Journal of Finance, 2009
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duffieEHS2009
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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)