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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…
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest…
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…
This paper presents comparison results and establishes risk bounds for credit portfolios within classes of Bernoulli mixture models, assuming conditionally independent defaults that are stochastically increasing with a common risk factor.…
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given…
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…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
The recent "correlation breakdown" in the modeling of credit default swaps, in which model correlations had to exceed 100% in order to reproduce market prices of supersenior tranches, is analyzed and argued to be a fundamental market…
In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the…
We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events…
We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model…
This econophysics work studies the long-range Ising model of a finite system with $N$ spins and the exchange interaction $\frac{J}{N}$ and the external field $H$ as a modely for homogeneous credit portfolio of assets with default…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
This paper considers mutual obligations in the interconnected bank system and analyzes their influence on joint and marginal survival probabilities as well as CDS and FTD prices for the individual banks. To make the role of mutual…
A standard quantitative method to access credit risk employs a factor model based on joint multivariate normal distribution properties. By extending a one-factor Gaussian copula model to make a more accurate default forecast, this paper…
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties…
This paper studies the consequences of capturing non-linear dependence among the covariates that drive the default of different obligors and the overall riskiness of their credit portfolio. Joint default modeling is, without loss of…
Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable…
The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli random…
In undirected graphical models, learning the graph structure and learning the functions that relate the predictive variables (features) to the responses given the structure are two topics that have been widely investigated in machine…