Download or read book Copula Based Multivariate Models with Applications to Risk Management and Insurance written by Marco Bee and published by . This book was released on 2005 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper consists in analysing the relevance of dependence concepts in finance, insurance and risk management, exploring how these concepts can be implemented in a statistical model via copula functions and pointing out some difficulties related to this methodology. In particular, we first review the statistical models currently used in the actuarial and financial fields when dealing with loss data; then we show, by means of two risk management applications, that copula-based models are very flexible but sometimes difficult to set up and to estimate; finally we study, by means of a simulation experiment, the properties of the maximum likelihood estimators of the Gaussian and Gumbel copula.

Download or read book Contributions to Static and Time varying Copula based Modeling of Multivariate Association written by Martin Ruppert and published by BoD – Books on Demand. This book was released on 2012 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Putting a particular emphasis on nonparametric methods that rely on modern empirical process techniques, the author contributes to the theory of static and time-varying stochastic models for multivariate association based on the concept of copulas. These functions enable a profound understanding of multivariate association, which is pivotal for judging whether a large set of risky assets entails diversification effects or aggravates risk from an entrepreneurial point of view. Since serial dependence is a stylized fact of financial time series, an asymptotic theory for estimating the structure of association in this context is developed under weak assumptions. A new measure of multivariate association, based on a notion of distance to stochastic independence, is introduced. Asymptotic results as well as hypothesis tests are established which are directly applicable to important types of multivariate financial time series. To ensure that risk management properly captures the current structure of association, it is crucial to assess the constancy of the structure. Therefore, nonparametric tests for a constant copula with either a specified or unspecified change point (candidate) are derived. The thesis concludes with a study of characterizations of association between non-continuous random variables.

Download or read book A Multivariate Claim Count Model for Applications in Insurance written by Daniela Anna Selch and published by Springer. This book was released on 2018-08-31 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications. Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions. Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Download or read book Copulae and Multivariate Probability Distributions in Finance written by Alexandra Dias and published by Routledge. This book was released on 2013-08-21 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.

Download or read book Statistical Inference for Copula and Tail Copula Models with Applications to Finance and Insurance written by Liang Peng and published by Chapman & Hall/CRC. This book was released on 2018-12-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will cover statistical inference for copula and tail copula models with applications in finance, insurance and risk management. After giving a quick introduction to copula and tail copula models, it will focus on various up-to-date statistical inference procedures, including point and interval estimation and goodness-of- t tests, for both copulas and tail copulas based on either independent data or dependent data. A chapter on applications in nance, insurance and risk management will be provided with R code.

Download or read book Multivariate Stochastic Copula based Deterioration Models in Infrastructure Economic Risk Management written by Wei Wang and published by . This book was released on 2010 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Copulae in Mathematical and Quantitative Finance written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2013-06-18 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.

Download or read book Archimedean Copula Based Models in Financial Risk Management written by Qing Xu and published by LAP Lambert Academic Publishing. This book was released on 2009-06-14 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copula is used to model multivariate data, as it accounts for the dependence structure and provides a flexible representation of the multivariate distribution. Recently a large number of Archimedean copulas have been proposed to deal with various dependence aspects in financial risk management, which invokes several new questions in some important yet under-researched areas.This dissertation comprises three essays and probes into three untouched questions all involving the Archimedean-copula-based models. It provides important empirical evidences that the Archimedean copula-based PVaR model generally has better forecasting performance than the Gaussian copula-based PVaR model. Therefore, financial risk managers should consider the use of the Archimedean copula-based PVaR model when attempting to forecast extreme downside dependent risk.

Download or read book Multivariate GARCH and Dynamic Copula Models for Financial Time Series written by Martin Grziska and published by Pro BUSINESS. This book was released on 2015-02-05 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents several non-parametric and parametric models for estimating dynamic dependence between financial time series and evaluates their ability to precisely estimate risk measures. Furthermore, the different dependence models are used to analyze the integration of emerging markets into the world economy. In order to analyze numerous dependence structures and to discover possible asymmetries, two distinct model classes are investigated: the multivariate GARCH and Copula models. On the theoretical side a new dynamic dependence structure for multivariate Archimedean Copulas is introduced which lifts the prevailing restriction to two dimensions and extends the multivariate dynamic Archimedean Copulas to more than two dimensions. On this basis a new mixture copula is presented using the newly invented multivariate dynamic dependence structure for the Archimedean Copulas and mixing it with multivariate elliptical copulas. Simultaneously a new process for modeling the time-varying weights of the mixture copula is introduced: this specification makes it possible to estimate various dependence structures within a single model. The empirical analysis of different portfolios shows that all equity portfolios and the bond portfolios of the emerging markets exhibit negative asymmetries, i.e. increasing dependence during market downturns. However, the portfolio consisting of the developed market bonds does not show any negative asymmetries. Overall, the analysis of the risk measures reveals that parametric models display portfolio risk more precisely than non-parametric models. However, no single parametric model dominates all other models for all portfolios and risk measures. The investigation of dependence between equity and bond portfolios of developed countries, proprietary, and secondary emerging markets reveals that secondary emerging markets are less integrated into the world economy than proprietary. Thus, secondary emerging markets are moresuitable to diversify a portfolio consisting of developed equity or bond indices than proprietary.

Download or read book Copula Based Risks Classification Models for General Insurance written by Joseph Kyalo Mung'atu and published by LAP Lambert Academic Publishing. This book was released on 2015-03-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In risk classification, similar risks should be assigned to the same class with respect to each variable to ease their management. The dependencies among the risks are examined by fitting copulas, estimating the dependence parameters and lastly using distance matrices to cluster the risks together. Distances used in the classification were determined by the problem at hand. The empirical study derived its data from the general insurance business in Kenya where the risks were classified by the Copula based approach. The motivation of the study was driven by the fact that insurance companies had collapsed in the past, one reason being the type of business classes they collectively engaged in. It is therefore important to understand the dependencies between risks for better risk management. This work proposed the use of the upper tail dependence, measured by the tail index, derived from the dependence parameter in determining the retention limits for a re-insurance arrangement. This will ensure that the highly dependent risks in the upper tail will forward higher proportion to the re-insurer and vice versa.

Download or read book Introduction to Bayesian Estimation and Copula Models of Dependence written by Arkady Shemyakin and published by John Wiley & Sons. This book was released on 2017-02-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.

Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.

Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka

Download or read book Managing Currency Risk written by Alexandre Beaulne and published by . This book was released on 2012 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Economic Time Series written by William R. Bell and published by CRC Press. This book was released on 2018-11-14 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Time Series: Modeling and Seasonality is a focused resource on analysis of economic time series as pertains to modeling and seasonality, presenting cutting-edge research that would otherwise be scattered throughout diverse peer-reviewed journals. This compilation of 21 chapters showcases the cross-fertilization between the fields of time s

Download or read book On Copula Density Estimation and Measures of Multivariate Association written by Thomas Blumentritt and published by BoD – Books on Demand. This book was released on 2012 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measuring the degree of association between random variables is a task inherent in many practical applications such as risk management and financial modeling. Well-known measures like Spearman's rho and Kendall's tau can be expressed in terms of the underlying copula only, hence, being independent of the underlying univariate marginal distributions. Opposed to these classical measures of association, mutual information, which is derived from information theory, constitutes a fundamentally different approach of measuring association. Although this measure is likewise independent of the univariate margins, it is not a functional of the copula but of the corresponding copula density. Besides the theoretical properties of mutual information as a measure of multivariate association, possibilities to estimate the copula density based on observations of continuous distributions are investigated. To cope with the effect of boundary bias, new estimators are introduced and existing functionals are generalized to the multivariate case. The performance of these estimators is evaluated in comparison to common kernel density estimation schemes. To facilitate variance estimation by means of resampling methods like bootstrapping, an algorithm is introduced, which significantly reduces computation time in comparison with pre-implemented algorithms. In practical applications, complete continuous data is oftentimes not available to the analyst. Instead, categorial data derived from the underlying continuous distribution may be given. Hence, estimation of the copula and its density based on contingency tables is investigated. The newly developed estimators are employed to derive estimates of Spearman's rho and Kendall's tau and their performance is compared.