Copula (probability theory)

About: Copula (probability theory) is a research topic. Over the lifetime, 4260 publications have been published within this topic receiving 65053 citations. The topic is also known as: Copula (probability theory).

Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls

Abstract: Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed.

Analysis of Multivariate Survival Data

Abstract: Introduction * Univariate Survival Data * Dependence Structures * Bivariate Dependence Measures * Probability Aspects of Multi-state Models * Statistical Inference for Multi-state Models * Shared Frailty Models * Statistical Inference for Shared Frailty Models * Shared Frailty Models for Recurrent Events * Multivariate Frailty Models * Instantaneous and Short-term Frailty Models * Competing Risks Models * Marginal and Copula Modelling * Multivariate Non-Parametric Estimates * Summary

On Default Correlation: A Copula Function Approach

Abstract: This paper studies the problem of default correlation. We first introduce a random variable called "time-until-default" to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. The definition and some basic properties of copula functions are given. We show that the current CreditMetrics approach to default correlation through asset correlation is equivalent to using a normal copula function. Finally, we give some numerical examples to illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

On Default Correlation: A Copula Function Approach

Abstract: This article studies the problem of default correlation. It introduces a random variable called “time-until-default” to denote the survival time of each defaultable entity or financial instrument, and defines the default correlation between two credit risks as the correlation coefficient between their survival times. The author explains why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. He shows that the current approach to default correlation through asset correlation is equivalent to using a normal copula function. Numerical examples illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

Econometric Analysis of Count Data

Abstract: The book provides graduate students and researchers with an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution models. Proper count data probability models allow for rich inferences, both with respect to the stochastic count process that generated the data, and with respect to predicting the distribution of outcomes. The book starts with a presentation of the benchmark Poisson regression model. Alternative models address unobserved heterogeneity, state dependence, selectivity, endogeneity, underreporting, and clustered sampling. Testing and estimation is discussed from frequentist and Bayesian perspectives. Finally, applications are reviewed in fields such as economics, marketing, sociology, demography, and health sciences.The fifth edition contains several new topics, including copula functions, Poisson regression for non-counts, additional semi-parametric methods, and discrete factor models. Other sections have been reorganized, rewritten, and extended.