A Hierarchical Archimedean Copula For Portfolio Credit Risk Modelling
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A Hierarchical Archimedean Copula for Portfolio Credit Risk Modelling by Natalia Puzanova Pdf
I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio.
A Hierarchical Model of Tail Dependent Asset Returns for Assessing Portfolio Credit Risk by Natalia Puzanova Pdf
This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting.
Credit Securitisations and Derivatives by Daniel Rösch,Harald Scheule Pdf
A comprehensive resource providing extensive coverage of the state of the art in credit secruritisations, derivatives, and risk management Credit Securitisations and Derivatives is a one-stop resource presenting the very latest thinking and developments in the field of credit risk. Written by leading thinkers from academia, the industry, and the regulatory environment, the book tackles areas such as business cycles; correlation modelling and interactions between financial markets, institutions, and instruments in relation to securitisations and credit derivatives; credit portfolio risk; credit portfolio risk tranching; credit ratings for securitisations; counterparty credit risk and clearing of derivatives contracts and liquidity risk. As well as a thorough analysis of the existing models used in the industry, the book will also draw on real life cases to illustrate model performance under different parameters and the impact that using the wrong risk measures can have.
Introduction to Bayesian Estimation and Copula Models of Dependence by Arkady Shemyakin,Alexander Kniazev Pdf
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.
Introduction to Credit Risk Modeling by Christian Bluhm,Ludger Overbeck,Christoph Wagner Pdf
Contains Nearly 100 Pages of New MaterialThe recent financial crisis has shown that credit risk in particular and finance in general remain important fields for the application of mathematical concepts to real-life situations. While continuing to focus on common mathematical approaches to model credit portfolios, Introduction to Credit Risk Modelin
Modern Financial Engineering: Counterparty, Credit, Portfolio And Systemic Risks by Giuseppe Orlando,Michele Bufalo,Henry Penikas,Concetta Zurlo Pdf
The book offers an overview of credit risk modeling and management. A three-step approach is adopted with the contents, after introducing the essential concepts of both mathematics and finance.Initially the focus is on the modeling of credit risk parameters mainly at the level of individual debtor and transaction, after which the book delves into counterparty credit risk, thus providing the link between credit and market risks. The second part is aimed at the portfolio level when multiple loans are pooled and default correlation becomes an important factor to consider and model. In this respect, the book explains how copulas help in modeling. The final stage is the macro perspective when the combination of credit risks related to financial institutions produces systemic risk and affects overall financial stability.The entire approach is two-dimensional as well. First, all modeling steps have replicable programming codes both in R and Matlab. In this way, the reader can experience the impact of changing the default probabilities of a given borrower or the weights of a sector. Second, at each stage, the book discusses the regulatory environment. This is because, at times, regulation can have stricter constraints than the outcome of internal models. In summary, the book guides the reader in modeling and managing credit risk by providing both the theoretical framework and the empirical tools necessary for a modern finance professional. In this sense, the book is aimed at a wide audience in all fields of study: from quants who want to engage in finance to economists who want to learn about coding and modern financial engineering.
Financial Engineering with Copulas Explained by J. Mai,M. Scherer Pdf
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.
Econometrics and Risk Management by Thomas B. Fomby,Jean-Pierre Fouque,Knut Solna Pdf
Covers credit risk and credit derivatives. This book offers several points of view on credit risk when looked at from the perspective of Econometrics and Financial Mathematics. It addresses the challenge of modeling defaults and their correlations, and results on copula, reduced form and structural models, and the top-down approach.
Concentration Risk in Credit Portfolios by Eva Lütkebohmert Pdf
Modeling and management of credit risk are the main topics within banks and other lending institutions. Historical experience shows that, in particular, concentration of risk in credit portfolios has been one of the major causes of bank distress. Therefore, concentration risk is highly relevant to anyone who wants to go beyond the very basic portfolio credit risk models. The book gives an introduction to credit risk modeling with the aim to measure concentration risks in credit portfolios. Taking the basic principles of credit risk in general as a starting point, several industry models are studied. These allow banks to compute a probability distribution of credit losses at the portfolio level. Besides these industry models the Internal Ratings Based model, on which Basel II is based, is treated. On the basis of these models various methods for the quantification of name and sector concentration risk and the treatment of default contagion are discussed. The book reflects current research in these areas from both an academic and a supervisory perspective
Credit Correlation by Alexander Lipton,Andrew Rennie Pdf
The recent growth of credit derivatives has been explosive. The global credit derivatives market grew in notional value from $1 trillion to $20 trillion from 2000 to 2006. However, understanding the true nature of these instruments still poses both theoretical and practical challenges. For a long time now, the framework of Gaussian copulas parameterized by correlation, and more recently base correlation, has provided an adequate, if unintuitive, description of the market. However, the increased liquidity in credit indices and index tranches, as well as the proliferation of exotic instruments such as forward starting tranches, options on tranches, leveraged super senior tranches, and the like, have made it imperative to come up with models that describe market reality better. This book, originally and concurrently published in the International Journal of Theoretical and Applied Finance, Vol. 10, No. 4, 2007, agrees that base correlation has outlived its usefulness; opinions of how to replace it, however, are divided. Both the top-down and bottom-up approaches for describing the dynamics of credit baskets are presented, and pro and contra arguments are put forward. Readers will decide which direction is the most promising one at the moment. However, it is hoped that, in the near future, models that transcend base correlation will be proposed and accepted by the market. Sample Chapter(s). Introduction (31 KB). Chapter 1: L(r)vy Simples Tructural Models (209 KB). Contents: L(r)vy Simple Structural Models (M Baxter); Cluster-Based Extension of the Generalized Poisson Loss Dynamics and Consistency with Single Names (D Brigo et al.); Stochastic Intensity Modeling for Structured Credit Exotics (A Chaposvsky et al.); Large Portfolio Credit Risk Modeling (M H A Davis & J C Esparragoza-Rodriguez); Empirical Copulas for CDO Tranche Pricing Using Relative Entropy (M A H Dempster et al.); Pricing and Hedging in a Dynamic Credit Model (Y Elouerkhaoui); Joint Distributions of Portfolio Losses and Exotic Portfolio Products (F Epple et al.); On the Term Structure of Loss Distributions: A Forward Model Approach (J Sidenius). Readership: Professionals, academics and students in the areas of finance and bank
Collateralized Debt Obligations by Enrico Marcantoni Pdf
The author focuses on a method to price Collateralized Debt Obligations (CDO) tranches. The original method is developed by Castagna, Mercurio and Mosconi in 2012. The Thesis provides an extension of the original work by generalizing the Gaussian dependence in terms of Copula functions. In particular the model is rewritten for the specific case of the Clayton copula. The method is applied to price the tranches of a CDX. By comparing the tranches prices, it is possible to notice that the Clayton approach leads to smaller equity and mezzanine tranches. The senior and super senior tranches levels are higher when the dependence is modeled by a Clayton copula.
Innovations in Quantitative Risk Management by Kathrin Glau,Matthias Scherer,Rudi Zagst Pdf
Quantitative models are omnipresent –but often controversially discussed– in todays risk management practice. New regulations, innovative financial products, and advances in valuation techniques provide a continuous flow of challenging problems for financial engineers and risk managers alike. Designing a sound stochastic model requires finding a careful balance between parsimonious model assumptions, mathematical viability, and interpretability of the output. Moreover, data requirements and the end-user training are to be considered as well. The KPMG Center of Excellence in Risk Management conference Risk Management Reloaded and this proceedings volume contribute to bridging the gap between academia –providing methodological advances– and practice –having a firm understanding of the economic conditions in which a given model is used. Discussed fields of application range from asset management, credit risk, and energy to risk management issues in insurance. Methodologically, dependence modeling, multiple-curve interest rate-models, and model risk are addressed. Finally, regulatory developments and possible limits of mathematical modeling are discussed.
Structured Credit Portfolio Analysis, Baskets and CDOs by Christian Bluhm,Ludger Overbeck Pdf
The financial industry is swamped by credit products whose economic performance is linked to the performance of some underlying portfolio of credit-risky instruments, like loans, bonds, swaps, or asset-backed securities. Financial institutions continuously use these products for tailor-made long and short positions in credit risks. Based on a stead
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 facto
