A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes

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

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

Interferon alpha-2a Plus Ribavirin 1,000/1,200 mg versus Interferon alpha-2a Plus Ribavirin 600 mg for Chronic Hepatitis C Infection in Patients on Opiate Maintenance Treatment: An Open-Label Randomized Multicenter Trial

Abstract : Background: : Many intravenous opiate users are infected with hepatitis C virus (HCV) but few are treated. Although this complies with various guidelines, virtually no published evidence supports such a recommendation. Patients and Methods: : In a multicenter study, HCV-infected patients in opiate maintenance treatment programs received interferon plus high- or low-dose ribavirin (1,000/1,200 mg or 600 mg). HIV-coinfected patients were not included. Endpoints were feasibility, efficacy, side effects, and reasons for dropout. Results: : Of the 420 patients who tested positive for HCV, 27 (6%) were enrolled; 393 (94%) either failed to meet the inclusion criteria or refused treatment. Virologic end-of-treatment response was achieved in 12/27 patients, and sustained response in 13/27 (48%). Response depended on viral genotype, not ribavirin dose. The two doses of ribavirin did not differ in their side effects. Conclusion: : In a small fraction of HCV-infected intravenous drug users in an opiate maintenance treatment program, antiviral therapy was feasible, safe, and effective. The success rate was comparable to that achieved in controlled studies that excluded drug user

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

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

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Sampling from Archimedean copulas

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution, to the distribution whose Laplace transform yields the copula generating function. In the infinite-dimensional limit there is a direct connection between the distribution of the copula value and the inverse Laplace transform. Armed with these results, we present three sampling algorithms, all of which entail drawing from a one-dimensional distribution and then scaling the result to create random deviates distributed according to the copula. We implement and compare the various methods. For more general cases, in which an N-dimensional Archimedean copula is given by N-1 nested generating functions, we present algorithms in which each new variate is drawn conditional only on the value of the copula of the previously drawn variates. We also discuss the use of composite nested and exchangeable copulas for modelling random variates with a natural hierarchical structure, such as ratings and sectors for obligors in credit baskets.

Swiss multicenter study evaluating the efficacy, feasibility and safety of peginterferon-alfa-2a and ribavirin in patients with chronic hepatitis C in official opiate substitution programs

BACKGROUND: Though patients in opiate substitution programs are commonly infected with HCV, due to safety and efficacy concerns, they are rarely treated with interferon and ribavirin. METHODS: In a multicenter study, HCV-infected patients in opiate maintenance treatment programs received 180 microg pegylated interferon-alfa-2a once weekly, plus daily ribavirin for 24 weeks (genotypes 2, 3), or 48 weeks (genotypes 1, 4). RESULTS: Of the 67 patients enrolled, 31 (46%) had HCV genotypes 1 or 4, and 36 (54%) had genotypes 2 or 3. Intent-to-treat analysis showed end-of-treatment virologic response in 75% of patients (81% of genotypes 2 or 3; 65% of genotypes 1 or 4), and a sustained virologic response in 61% of patients (72% of genotypes 2 or 3; 48% of genotypes 1 or 4). Fifteen patients (22%) did not complete the study, in 5 (8%) cases because of severe adverse events. CONCLUSIONS: Drug users with chronic HCV infection, regularly attending an opiate maintenance program in which close collaboration between hepatologists/internists and addiction specialists is assured, can be treated effectively and safely with pegylated interferon-alfa-2a and ribavirin. Treatment results are very similar to those in other patient groups, and thus therapy should also be considered for this population