A Voter Model for Credit Contagion

In this chapter we want to emphasize the virtue of statistical mechanics approaches to socio-economics and, in particular, to the modeling of credit contagion phenomena. As it is shown in recent articles, for example by [22] in their famous binary choice models, there is a close relation between socio-economics and statistical mechanics. This motivates the use of interacting particle systems also in finance. The approach stems from the belief that the social or local structure among agents can be formalized. Local interactions are mediated by a social structure, not by the market. Moreover, this approach to local interactions is non-strategic but probabilistic. A general problem in these kinds of models – but not to be considered here – is that of phase transition, referring to the non-uniqueness of the ruling probability measure in the random economic system. In this sense, local data may not uniquely specify the global behavior of the system, as for example in the famous Ising model that is elaborately discussed in [66]. Moreover, these models necessitate a quite naive view of agents when paralleling models of the unlived nature in economics. This, however, can also constitute a great advantage as models from interacting particle systems do not require any rationality assumptions on agents.