Non-existence of Markovian time dynamics for graphical models of correlated default
AbstractFiliz et al. (2008) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph, where the vertices correspond to the firms and the edges describe the network of interdependencies between the firms, a parameter for each vertex that captures the individual propensity of that firm to default, and a parameter for each edge that captures the joint propensity of the two connected firms to default. The correlated default model can be re-rewritten as a standard Ising model on the graph by identifying the set of defaulting firms in the default model with the set of sites in the Ising model for which the spin is +1. We ask whether there is a suitable continuous time Markov chain taking values in the subsets of the vertex set such that the initial state of the chain is the empty set, each jump of the chain involves the inclusion of a single extra vertex, the distribution of the chain at some fixed time horizon time is the one given by the default model, and the distribution of the chain for other times is described by a probability distribution in the same family as the default model. We show for three simple but financially natural special cases that this is not possible outside of the trivial case where there is complete independence between the firms.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1008.2226.
Date of creation: Aug 2010
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jorion, Philippe & Zhang, Gaiyan, 2007. "Good and bad credit contagion: Evidence from credit default swaps," Journal of Financial Economics, Elsevier, vol. 84(3), pages 860-883, June.
- Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007.
"Common Failings: How Corporate Defaults Are Correlated,"
Journal of Finance,
American Finance Association, vol. 62(1), pages 93-117, 02.
- Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.