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Sampling Nested Archimedean Copulas
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Author :Jan Marius Hofert Publisher :Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN 13 :9783838116563 Total Pages :200 pages Book Rating :4.1/5 (165 download)
Book Synopsis Sampling Nested Archimedean Copulas by : Jan Marius Hofert
Download or read book Sampling Nested Archimedean Copulas written by Jan Marius Hofert and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2010 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are distribution functions with standard uniform univariate margins. A famous class of copulas consists of Archimedean copulas, which are constructed by a one-dimensional function called the generator of the Archimedean copula. In large-dimensional applications the symmetry of Archimedean copulas is often considered to be a drawback. By nesting Archimedean copulas at different levels, one obtains the more general and flexible class of nested Archimedean copulas. The present work explores these copulas. In particular, efficient sampling algorithms, especially suited for large dimensions, are presented. From the practitioner's point of view, fast sampling algorithms are required for large-scale simulation studies. Efficiently sampling nested Archimedean copulas requires sampling from certain distributions which are related to the generators of the Archimedean copulas involved via Laplace-Stieltjes transforms. The work at hand presents efficient strategies for sampling these distributions. As an application, a pricing model for collateralized debt obligations is developed which precisely captures the given hierarchical structure of such a credit-risky portfolio.
Book Synopsis Sampling Nested Archimedean Copulas with Applications to CDO Pricing by : Marius Hofert
Download or read book Sampling Nested Archimedean Copulas with Applications to CDO Pricing written by Marius Hofert and published by . This book was released on 2010 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hierarchical Archimedean Copulas by : Jan Górecki
Download or read book Hierarchical Archimedean Copulas written by Jan Górecki and published by Springer Nature. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition) by : Jan-frederik Mai
Download or read book Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition) written by Jan-frederik Mai and published by #N/A. This book was released on 2017-06-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book remains a valuable tool both for statisticians who are already familiar with the theory of copulas and just need to develop sampling algorithms, and for practitioners who want to learn copulas and implement the simulation techniques needed to exploit the potential of copulas in applications.'Mathematical ReviewsThe book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.
Book Synopsis Copula Theory and Its Applications by : Piotr Jaworski
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.
Book Synopsis Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications by : Matthias Scherer
Download or read book Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications written by Matthias Scherer and published by World Scientific. This book was released on 2012-06-26 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.
Book Synopsis Elements of Copula Modeling with R by : Marius Hofert
Download or read book Elements of Copula Modeling with R written by Marius Hofert and published by Springer. This book was released on 2019-01-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
Book Synopsis Dependence Modeling with Copulas by : Harry Joe
Download or read book Dependence Modeling with Copulas written by Harry Joe and published by CRC Press. This book was released on 2014-06-26 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.
Book Synopsis Copulas and Their Applications in Water Resources Engineering by : Lan Zhang
Download or read book Copulas and Their Applications in Water Resources Engineering written by Lan Zhang and published by Cambridge University Press. This book was released on 2019-01-10 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustration of copula theory with detailed real-world case study examples in the fields of hydrology and water resources engineering.
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
Book Synopsis Dynamic Copula Methods in Finance by : Umberto Cherubini
Download or read book Dynamic Copula Methods in Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2011-10-20 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest tools and techniques for pricing and risk management This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration.
Book Synopsis Site Diversity in Satellite Communications by : Arsim Kelmendi
Download or read book Site Diversity in Satellite Communications written by Arsim Kelmendi and published by Springer Nature. This book was released on 2023-04-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes multi-site diversity modelling of induced rain attenuation statistics for satellite communication systems using copula functions. It gathers all relevant state-of-the-art knowledge, provides the missing pieces and rounds them up in a way that the reader is given a complete picture of important modelling factors and ways to address them. The books’ main features include: Data post-processing methodology for statistical analysis based on our Earth-satellite propagation experiments. Two novel multi-site diversity prediction models based on Gaussian copula considering distance between stations or considering distance, baseline, and elevation angle. Two novel multi-site diversity prediction models based on hyperbolic cosecant copula considering distance between stations or considering distance, baseline, and elevation angle. Exhaustive comparative tests and error performance of the prediction models showing that improved error performance is achieved compared to the ITU R model and to the state-of-the-art models. The results presented in the book are expected to contribute to the improvement of the system design and to the further research of modelling the next generation satellite links at higher frequencies.
Book Synopsis Pricing and Liquidity of Complex and Structured Derivatives by : Mathias Schmidt
Download or read book Pricing and Liquidity of Complex and Structured Derivatives written by Mathias Schmidt and published by Springer. This book was released on 2016-10-31 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the “strike of default” (SOD) benchmark concept. The author determines the SOD through cross-sectional pricing between the credit market and the option market, considering the same underlying. The idea of the SOD is to combine the implied probability of default from both markets to get a time-depending share price, at which the markets believe the underlying will default. By means of credit default swaps (CDS) and option pricing methods, the SOD is determined for any exchange-listed company, where option and CDS market data are available.
Book Synopsis Basic Elements of Computational Statistics by : Wolfgang Karl Härdle
Download or read book Basic Elements of Computational Statistics written by Wolfgang Karl Härdle and published by Springer. This book was released on 2017-09-29 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational statistics presents tools and concepts of univariate and multivariate statistical data analysis with a strong focus on applications and implementations in the statistical software R. It covers mathematical, statistical as well as programming problems in computational statistics and contains a wide variety of practical examples. In addition to the numerous R sniplets presented in the text, all computer programs (quantlets) and data sets to the book are available on GitHub and referred to in the book. This enables the reader to fully reproduce as well as modify and adjust all examples to their needs. The book is intended for advanced undergraduate and first-year graduate students as well as for data analysts new to the job who would like a tour of the various statistical tools in a data analysis workshop. The experienced reader with a good knowledge of statistics and programming might skip some sections on univariate models and enjoy the various ma thematical roots of multivariate techniques. The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allows readers to reproduce the tables, pictures and calculations inside this Springer book.
Book Synopsis Financial Engineering with Copulas Explained by : J. Mai
Download or read book Financial Engineering with Copulas Explained written by J. Mai and published by Springer. This book was released on 2014-10-02 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a succinct guide to the application and modelling of dependence models or copulas in the financial markets. First applied to credit risk modelling, copulas are now widely used across a range of derivatives transactions, asset pricing techniques and risk models and are a core part of the financial engineer's toolkit.
Book Synopsis Copulae and Multivariate Probability Distributions in Finance by : Alexandra Dias
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 206 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.
Book Synopsis Fundamental Aspects of Operational Risk and Insurance Analytics by : Marcelo G. Cruz
Download or read book Fundamental Aspects of Operational Risk and Insurance Analytics written by Marcelo G. Cruz and published by John Wiley & Sons. This book was released on 2015-01-20 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.
