74 research outputs found
Correlated Binomial Models and Correlation Structures
We discuss a general method to construct correlated binomial distributions by
imposing several consistent relations on the joint probability function. We
obtain self-consistency relations for the conditional correlations and
conditional probabilities. The beta-binomial distribution is derived by a
strong symmetric assumption on the conditional correlations. Our derivation
clarifies the 'correlation' structure of the beta-binomial distribution. It is
also possible to study the correlation structures of other probability
distributions of exchangeable (homogeneous) correlated Bernoulli random
variables. We study some distribution functions and discuss their behaviors in
terms of their correlation structures.Comment: 12 pages, 7 figure
Evaluation of Tranche in Securitization and Long-range Ising Model
This econophysics work studies the long-range Ising model of a finite system
with spins and the exchange interaction and the external
field as a modely for homogeneous credit portfolio of assets with default
probability and default correlation . Based on the discussion
on the phase diagram, we develop a perturbative calculation method for
the model and obtain explicit expressions for and the
normalization factor in terms of the model parameters and . The
effect of the default correlation on the probabilities
for defaults and on the cumulative distribution
function are discussed. The latter means the average loss rate
of the``tranche'' (layered structure) of the securities (e.g. CDO), which are
synthesized from a pool of many assets. We show that the expected loss rate of
the subordinated tranche decreases with and that of the senior
tranche increases linearly, which are important in their pricing and ratings.Comment: 21 pages, 9 figure
Infectious Default Model with Recovery and Continuous Limit
We introduce an infectious default and recovery model for N obligors.
Obligors are assumed to be exchangeable and their states are described by N
Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying
independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery
infections are described by Y_{ij} and Y'_{ij}. We obtain the default
probability function P(k) for k defaults. Taking its continuous limit, we find
two nontrivial probability distributions with the reflection symmetry of S_{i}
\leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we
understand it theoretically. We also compare P(k) with an implied default
distribution function inferred from the quotes of iTraxx-CJ. In order to
explain the behavior of the implied distribution, the recovery effect may be
necessary.Comment: 13 pages, 7 figure
Correlation Structures of Correlated Binomial Models and Implied Default Distribution
We show how to analyze and interpret the correlation structures, the
conditional expectation values and correlation coefficients of exchangeable
Bernoulli random variables. We study implied default distributions for the
iTraxx-CJ tranches and some popular probabilistic models, including the
Gaussian copula model, Beta binomial distribution model and long-range Ising
model. We interpret the differences in their profiles in terms of the
correlation structures. The implied default distribution has singular
correlation structures, reflecting the credit market implications. We point out
two possible origins of the singular behavior.Comment: 16 pages, 7 figure
Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios
This paper generalizes Moody's correlated binomial default distribution for
homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to
the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider
two cases. In the first case, we treat a portfolio whose assets have uniform
default correlation and non-uniform default probabilities. We obtain the
default probability distribution and study the effect of the inhomogeneity on
it. The second case corresponds to a portfolio with inhomogeneous default
correlation. Assets are categorized in several different sectors and the
inter-sector and intra-sector correlations are not the same. We construct the
joint default probabilities and obtain the default probability distribution. We
show that as the number of assets in each sector decreases, inter-sector
correlation becomes more important than intra-sector correlation. We study the
maximum values of the inter-sector default correlation. Our generalization
method can be applied to any correlated binomial default distribution model
which has explicit relations to the conditional default probabilities or
conditional default correlations, e.g. Credit Risk, implied default
distributions. We also compare some popular CDO pricing models from the
viewpoint of the range of the implied tranche correlation.Comment: 29 pages, 17 figures and 1 tabl
Low Energy Pion-Hyperon Interaction
We study the low energy pion-hyperon interaction considering effective
non-linear chiral invariant Lagrangians including pions, rho mesons, hyperons
and corresponding resonances. Then we calculate the S- and P-wave phase-shifts,
total cross sections, angular distributions and polarizations for the momentum
in the center-of-mass frame up to k=400 MeV. With these results we discuss the
CP violation in the csi-> pi-lambda and omega-> pi-csi weak decays.Comment: 10 pages, 10 figure
Lambda^0 polarization as a probe for production of deconfined matter in ultra-relativistic heavy-ion collisions
We study the polarization change of Lambda^0's produced in ultra-relativistic
heavy-ion collisions with respect to the polarization observed in proton-proton
collisions as a signal for the formation of a Quark-Gluon Plasma (QGP).
Assuming that, when the density of participants in the collision is larger than
the critical density for QGP formation, the Lambda^0 production mechanism
changes from recombination type processes to the coalescence of free valence
quarks, we find that the Lambda^0 polarization depends on the relative
contribution of each process to the total number of Lambda^0's produced in the
collision. To describe the polarization of Lambda^0's in nuclear collisions for
densities below the critical density for the QGP formation, we use the
DeGrand-Miettinen model corrected for the effects introduced by multiple
scattering of the produced Lambda^0 within the nuclear environment.Comment: 9 pages, 6 figures, uses ReVTeX and epsfig.st
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