504 research outputs found
Effects of Economic Interactions on Credit Risk
We study a credit risk model which captures effects of economic interactions
on a firm's default probability. Economic interactions are represented as a
functionally defined graph, and the existence of both cooperative, and
competitive, business relations is taken into account. We provide an analytic
solution of the model in a limit where the number of business relations of each
company is large, but the overall fraction of the economy with which a given
company interacts may be small. While the effects of economic interactions are
relatively weak in typical (most probable) scenarios, they are pronounced in
situations of economic stress, and thus lead to a substantial fattening of the
tails of loss distributions in large loan portfolios. This manifests itself in
a pronounced enhancement of the Value at Risk computed for interacting
economies in comparison with their non-interacting counterparts.Comment: 24 pages, 6 figure
The biology of the Isopoda of the region of Douglas Lake, Michigan (continuation).
http://deepblue.lib.umich.edu/bitstream/2027.42/51695/1/121.pd
Dynamic rewiring in small world networks
We investigate equilibrium properties of small world networks, in which both
connectivity and spin variables are dynamic, using replicated transfer matrices
within the replica symmetric approximation. Population dynamics techniques
allow us to examine order parameters of our system at total equilibrium,
probing both spin- and graph-statistics. Of these, interestingly, the degree
distribution is found to acquire a Poisson-like form (both within and outside
the ordered phase). Comparison with Glauber simulations confirms our results
satisfactorily.Comment: 21 pages, 5 figure
Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
We study the dynamics of macroscopic observables such as the magnetization
and the energy per degree of freedom in Ising spin models on random graphs of
finite connectivity, with random bonds and/or heterogeneous degree
distributions. To do so we generalize existing implementations of dynamical
replica theory and cavity field techniques to systems with strongly disordered
and locally tree-like interactions. We illustrate our results via application
to the dynamics of e.g. spin-glasses on random graphs and of the
overlap in finite connectivity Sourlas codes. All results are tested against
Monte Carlo simulations.Comment: 4 pages, 14 .eps file
Derivatives and Credit Contagion in Interconnected Networks
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a decade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure
Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
We study XY spin systems on small world lattices for a variety of graph
structures, e.g. Poisson and scale-free, superimposed upon a one dimensional
chain. In order to solve this model we extend the cavity method in the one
pure-state approximation to deal with real-valued dynamical variables. We find
that small-world architectures significantly enlarge the region in parameter
space where synchronization occurs. We contrast the results of population
dynamics performed on a truncated set of cavity fields with Monte Carlo
simulations and find excellent agreement. Further, we investigate the
appearance of replica symmetry breaking in the spin-glass phase by numerically
analyzing the proliferation of pure states in the message passing equations.Comment: 10 pages, 3 figure
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