2010/08/12 by Steven N. Evans, Evans, Steven N., Alexandru Hening +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60K35 (Primary) 91G40 #91B80 (Secondary) #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60K35 #msc:91B80 #msc:91G40 #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1008.2226
18 pages
arxiv created 2010/08/12 · openalex publication_date 2010/08/12 · arxiv updated 2010/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Filiz et al. (2008) proposed a model for the pattern of defaults seen among a\ngroup of firms at the end of a given time period. The ingredients in the model\nare a graph, where the vertices correspond to the firms and the edges describe\nthe network of interdependencies between the firms, a parameter for each vertex\nthat captures the individual propensity of that firm to default, and a\nparameter for each edge that captures the joint propensity of the two connected\nfirms to default. The correlated default model can be re-rewritten as a\nstandard Ising model on the graph by identifying the set of defaulting firms in\nthe default model with the set of sites in the Ising model for which the spin\nis +1. We ask whether there is a suitable continuous time Markov chain taking\nvalues in the subsets of the vertex set such that the initial state of the\nchain is the empty set, each jump of the chain involves the inclusion of a\nsingle extra vertex, the distribution of the chain at some fixed time horizon\ntime is the one given by the default model, and the distribution of the chain\nfor other times is described by a probability distribution in the same family\nas the default model. We show for three simple but financially natural special\ncases that this is not possible outside of the trivial case where there is\ncomplete independence between the firms.\n