  This paper develops the Jungle model in a credit portfolio framework. The
Jungle model is able to model credit contagion, produce doubly-peaked
probability distributions for the total default loss and endogenously generate
quasi phase transitions, potentially leading to systemic credit events which
happen unexpectedly and without an underlying single cause. We show the Jungle
model provides the optimal probability distribution for credit losses, under
some reasonable empirical constraints. The Dandelion model, a particular case
of the Jungle model, is presented, motivated and exactly solved. The Dandelion
model provides an explicit example of doubly-peaked probability distribution
for the credit losses. The Diamond model, another instance of the Jungle model,
experiences the so called quasi phase transitions; in particular, both the U.S.
subprime and the European sovereign crises are shown to be potential examples
of quasi phase transitions. We argue the three known sources of default
clustering (contagion, macroeconomic risk factors and frailty) can be
understood under the unifying framework of contagion. We suggest how the Jungle
model is able to explain a series of empirical stylized facts in credit
portfolios, hard to reconcile by some standard credit portfolio models. We show
the Jungle model can handle inhomogeneous portfolios with state-dependent
recovery rates. We look at model risk in a credit risk framework under the
Jungle model, especially in relation to systemic risks posed by doubly-peaked
distributions and quasi phase transitions.
