469 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
11 Aspects of Continuity and Transformation From the Research of Four Communities in Tushima Island
報告本稿は,当センター第一期個別共同研究「持続と変容の実態の研究 ―対馬60年を事例として」で実施した現地調査の報告である.報告の一部はすでに前年度『年報』第7号に「持続と変容の諸相― 四つの集落の聞き書きから(1)」として発表した.筆者の事情により報告の執筆が遅れたため,「調査報告」として(2)からはじまるという変則的な形になったが,これは,年報全体の編集方針に合わせて形式を変更したためであることをお断りしておきたい
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