Paweł Sieczka, Didier Sornette, Janusz A. Hołyst
posted by Matúš Medo
(9 February 2010)
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Inspired by the bankruptcy of Lehman Brothers and its consequences on the
global financial system, we develop a simple model in which
a83
the Lehman default
event is quantified as having an almost immediate effect in worsening the
credit worthiness of all financial institutions in the economic network. In our
stylized description, all properties of a given firm are captured by its
effective credit rating, which follows a simple dynamics of co-evolution with
the credit ratings of the other firms in our economic network. The dynamics
resembles the evolution of Potts spin-glass with external global field
corresponding to a panic effect in the economy. The existence of a global phase
transition, between paramagnetic and ferromagnetic phases, explains the large
susceptibility of the system to negative shocks. We show that bailing out the
first few defaulting firms does not solve the problem, but does have the effect
of alleviating considerably the global shock, as measured by the fraction of
firms that are not defaulting as a consequence. This beneficial effect is the
counterpart of the large vulnerability of the system of coupled firms, which
are both the direct consequences of the collective self-organized endogenous
behaviors of the credit ratings of the firms in our economic network.
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