Download or read book Copulae in Mathematical and Quantitative Finance written by Piotr Jaworski and published by Springer. This book was released on 2013-06-20 with total page 294 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 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 Copula Methods in Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2004-10-22 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications. It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis. Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues. Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions.

Download or read book Simulating Copulas written by Jan-Frederik Mai and published by World Scientific. This book was released on 2012 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.Errata(s)Errata (128 KB)

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.

Download or read book Copula Methods in Finance written by Umberto Cherubini and published by . This book was released on 2013 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications. It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis. Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues. Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions.

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 Applied Quantitative Finance written by Wolfgang Karl Härdle and published by Springer. This book was released on 2017-08-02 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides practical solutions and introduces recent theoretical developments in risk management, pricing of credit derivatives, quantification of volatility and copula modeling. This third edition is devoted to modern risk analysis based on quantitative methods and textual analytics to meet the current challenges in banking and finance. It includes 14 new contributions and presents a comprehensive, state-of-the-art treatment of cutting-edge methods and topics, such as collateralized debt obligations, the high-frequency analysis of market liquidity, and realized volatility. The book is divided into three parts: Part 1 revisits important market risk issues, while Part 2 introduces novel concepts in credit risk and its management along with updated quantitative methods. The third part discusses the dynamics of risk management and includes risk analysis of energy markets and for cryptocurrencies. Digital assets, such as blockchain-based currencies, have become popular b ut are theoretically challenging when based on conventional methods. Among others, it introduces a modern text-mining method called dynamic topic modeling in detail and applies it to the message board of Bitcoins. The unique synthesis of theory and practice supported by computational tools is reflected not only in the selection of topics, but also in the fine balance of scientific contributions on practical implementation and theoretical concepts. This link between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners convenient access to new techniques in quantitative finance. Hence the book will appeal both to researchers, including master and PhD students, and practitioners, such as financial engineers. The results presented in the book are fully reproducible and all quantlets needed for calculations are provided on an accompanying website. 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.

Download or read book Heavy Tails And Copulas Topics In Dependence Modelling In Economics And Finance written by Rustam Ibragimov and published by World Scientific. This book was released on 2017-02-24 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory.'Quantitative Finance This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.

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.

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 167 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.

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 Computational Methods for Quantitative Finance written by Norbert Hilber and published by Springer Science & Business Media. This book was released on 2013-02-15 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to Lévy, additive and certain classes of Feller processes. This book is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics.​

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 2017-03-20 with total page 314 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 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.

Download or read book Mathematical Statistics and Limit Theorems written by Marc Hallin and published by Springer. This book was released on 2015-04-07 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.

Download or read book An Introduction to Copulas written by Roger B. Nelsen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.