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Author : Lyn C. Thomas
Publisher : Unknown
Page : 25 pages
File Size : 46,5 Mb
Release : 1999
Category : Bonds
ISBN : 072980447X
Author : Lyn C. Thomas
Publisher : Unknown
Page : 36 pages
File Size : 40,9 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:1290403941
This paper provides a Markov chain model for the term structure and credit risk spreads of bond prices. It allows dependency between the stochastic process modeling the interest rate and the Markov chain process describing changes in the credit rating of the bonds by their mutual dependency on a hidden Markov chain, which can be thought of as describing the underlying economic conditions. The model also allows a new interpretation of risk premia used in previous approaches and also uses a linear programming approach to strip the bonds of their coupons in such a way as to guarantee there is no mis-pricing.
Author : P. C. G. Vassiliou
Publisher : John Wiley & Sons
Page : 296 pages
File Size : 49,9 Mb
Release : 2013-03-01
Category : Mathematics
ISBN : 9781118618660
Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives. Next, we use the discrete-time binomial model to introduce all relevant concepts. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. However, we do not expand beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated from the text for easy reference and identification, are included. The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk. This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.
Author : Tomasz R. Bielecki,Marek Rutkowski
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 50,8 Mb
Release : 2004-01-22
Category : Business & Economics
ISBN : 3540675930
The motivation for the mathematical modeling studied in this text on developments in credit risk research is the bridging of the gap between mathematical theory of credit risk and the financial practice. Mathematical developments are covered thoroughly and give the structural and reduced-form approaches to credit risk modeling. Included is a detailed study of various arbitrage-free models of default term structures with several rating grades.
Author : Ramaprasad Bhar,Shigeyuki Hamori
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 55,8 Mb
Release : 2006-04-18
Category : Business & Economics
ISBN : 9781402079405
Markov chains have increasingly become useful way of capturing stochastic nature of many economic and financial variables. Although the hidden Markov processes have been widely employed for some time in many engineering applications e.g. speech recognition, its effectiveness has now been recognized in areas of social science research as well. The main aim of Hidden Markov Models: Applications to Financial Economics is to make such techniques available to more researchers in financial economics. As such we only cover the necessary theoretical aspects in each chapter while focusing on real life applications using contemporary data mainly from OECD group of countries. The underlying assumption here is that the researchers in financial economics would be familiar with such application although empirical techniques would be more traditional econometrics. Keeping the application level in a more familiar level, we focus on the methodology based on hidden Markov processes. This will, we believe, help the reader to develop more in-depth understanding of the modeling issues thereby benefiting their future research.
Author : Ali Mohamad-Djafari
Publisher : John Wiley & Sons
Page : 369 pages
File Size : 54,8 Mb
Release : 2013-01-29
Category : Technology & Engineering
ISBN : 9781118600467
The concept of an inverse problem is a familiar one to most scientists and engineers, particularly in the field of signal and image processing, imaging systems (medical, geophysical, industrial non-destructive testing, etc.), and computer vision. In imaging systems, the aim is not just to estimate unobserved images but also their geometric characteristics from observed quantities that are linked to these unobserved quantities by a known physical or mathematical relationship. In this manner techniques such as image enhancement or addition of hidden detail can be delivered. This book focuses on imaging and vision problems that can be clearly described in terms of an inverse problem where an estimate for the image and its geometrical attributes (contours and regions) is sought. The book uses a consistent methodology to examine inverse problems such as: noise removal; restoration by deconvolution; 2D or 3D reconstruction in X-ray, tomography or microwave imaging; reconstruction of the surface of a 3D object using X-ray tomography or making use of its shading; reconstruction of the surface of a 3D landscape based on several satellite photos; super-resolution; motion estimation in a sequence of images; separation of several images mixed using instruments with different sensitivities or transfer functions; and much more.
Author : Carsten Wehn,Christian Hoppe,Greg N. Gregoriou
Publisher : Academic Press
Page : 652 pages
File Size : 44,9 Mb
Release : 2012-12-17
Category : Business & Economics
ISBN : 9780124158887
It is widely acknowledged that many financial modelling techniques failed during the financial crisis, and in our post-crisis environment many techniques are being reconsidered. This single volume provides a guide to lessons learned for practitioners and a reference for academics. Including reviews of traditional approaches, real examples, and case studies, contributors consider portfolio theory; methods for valuing equities and equity derivatives, interest rate derivatives, and hybrid products; and techniques for calculating risks and implementing investment strategies. Describing new approaches without losing sight of their classical antecedents, this collection of original articles presents a timely perspective on our post-crisis paradigm. Highlights pre-crisis best classical practices, identifies post-crisis key issues, and examines emerging approaches to solving those issues Singles out key factors one must consider when valuing or calculating risks in the post-crisis environment Presents material in a homogenous, practical, clear, and not overly technical manner
Author : AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFE,Ams-Ims-Siam Joint Summer Research Conference on Mathematics,George Yin,Qing Zhang
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 50,7 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780821834121
The mathematics of finance involves a wide spectrum of techniques that go beyond traditional applied mathematics. The field has witnessed a tremendous amount of progress in recent years, which has inspired communication and networking among researchers in finance, economics, engineering, and industry. This volume contains papers based on the talks given at the first AMS-IMS-SIAM joint research conference on financial mathematics. Topics covered include modeling, estimation, optimization, control, risk assessment and management, contingent claim pricing, dynamic hedging, and financial derivative design.
Author : Anonim
Publisher : Unknown
Page : 990 pages
File Size : 51,8 Mb
Release : 2000
Category : Risk management
ISBN : STANFORD:36105062163253
Author : Alexander Lipton,Andrew Rennie
Publisher : OUP Oxford
Page : 704 pages
File Size : 42,9 Mb
Release : 2013-01-17
Category : Business & Economics
ISBN : 9780191648250
From the late 1990s, the spectacular growth of a secondary market for credit through derivatives has been matched by the emergence of mathematical modelling analysing the credit risk embedded in these contracts. This book aims to provide a broad and deep overview of this modelling, covering statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modelling, and securitisation. Both reduced-form and firm-value models for the default of single entities are considered in detail, with extensive discussion of both their theoretical underpinnings and practical usage in pricing and risk. For multiple entity modelling, the now notorious Gaussian copula is discussed with analysis of its shortcomings, as well as a wide range of alternative approaches including multivariate extensions to both firm-value and reduced form models, and continuous-time Markov chains. One important case of multiple entities modelling - counterparty risk in credit derivatives - is further explored in two dedicated chapters. Alternative non-Gaussian approaches to modelling are also discussed, including extreme-value theory and saddle-point approximations to deal with tail risk. Finally, the recent growth in securitisation is covered, including house price modelling and pricing models for asset-backed CDOs. The current credit crisis has brought modelling of the previously arcane credit markets into the public arena. Lipton and Rennie with their excellent team of contributors, provide a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. Though technical in nature, the pros and cons of various approaches attempt to provide a balanced view of the role that mathematical modelling plays in the modern credit markets. This book will appeal to students and researchers in statistics, economics, and finance, as well as practitioners, credit traders, and quantitative analysts
Author : David Lando
Publisher : Princeton University Press
Page : 328 pages
File Size : 52,5 Mb
Release : 2009-12-13
Category : Business & Economics
ISBN : 9781400829194
Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk. David Lando considers the two broad approaches to credit risk analysis: that based on classical option pricing models on the one hand, and on a direct modeling of the default probability of issuers on the other. He offers insights that can be drawn from each approach and demonstrates that the distinction between the two approaches is not at all clear-cut. The book strikes a fruitful balance between quickly presenting the basic ideas of the models and offering enough detail so readers can derive and implement the models themselves. The discussion of the models and their limitations and five technical appendixes help readers expand and generalize the models themselves or to understand existing generalizations. The book emphasizes models for pricing as well as statistical techniques for estimating their parameters. Applications include rating-based modeling, modeling of dependent defaults, swap- and corporate-yield curve dynamics, credit default swaps, and collateralized debt obligations.
Author : Darrell Duffie,Kenneth J. Singleton
Publisher : Princeton University Press
Page : 416 pages
File Size : 49,6 Mb
Release : 2012-01-12
Category : Business & Economics
ISBN : 9781400829170
In this book, two of America's leading economists provide the first integrated treatment of the conceptual, practical, and empirical foundations for credit risk pricing and risk measurement. Masterfully applying theory to practice, Darrell Duffie and Kenneth Singleton model credit risk for the purpose of measuring portfolio risk and pricing defaultable bonds, credit derivatives, and other securities exposed to credit risk. The methodological rigor, scope, and sophistication of their state-of-the-art account is unparalleled, and its singularly in-depth treatment of pricing and credit derivatives further illuminates a problem that has drawn much attention in an era when financial institutions the world over are revising their credit management strategies. Duffie and Singleton offer critical assessments of alternative approaches to credit-risk modeling, while highlighting the strengths and weaknesses of current practice. Their approach blends in-depth discussions of the conceptual foundations of modeling with extensive analyses of the empirical properties of such credit-related time series as default probabilities, recoveries, ratings transitions, and yield spreads. Both the "structura" and "reduced-form" approaches to pricing defaultable securities are presented, and their comparative fits to historical data are assessed. The authors also provide a comprehensive treatment of the pricing of credit derivatives, including credit swaps, collateralized debt obligations, credit guarantees, lines of credit, and spread options. Not least, they describe certain enhancements to current pricing and management practices that, they argue, will better position financial institutions for future changes in the financial markets. Credit Risk is an indispensable resource for risk managers, traders or regulators dealing with financial products with a significant credit risk component, as well as for academic researchers and students.
Author : Stefan Trueck,Svetlozar T. Rachev
Publisher : Academic Press
Page : 279 pages
File Size : 50,5 Mb
Release : 2009-01-15
Category : Business & Economics
ISBN : 9780080920306
In the last decade rating-based models have become very popular in credit risk management. These systems use the rating of a company as the decisive variable to evaluate the default risk of a bond or loan. The popularity is due to the straightforwardness of the approach, and to the upcoming new capital accord (Basel II), which allows banks to base their capital requirements on internal as well as external rating systems. Because of this, sophisticated credit risk models are being developed or demanded by banks to assess the risk of their credit portfolio better by recognizing the different underlying sources of risk. As a consequence, not only default probabilities for certain rating categories but also the probabilities of moving from one rating state to another are important issues in such models for risk management and pricing. It is widely accepted that rating migrations and default probabilities show significant variations through time due to macroeconomics conditions or the business cycle. These changes in migration behavior may have a substantial impact on the value-at-risk (VAR) of a credit portfolio or the prices of credit derivatives such as collateralized debt obligations (D+CDOs). In Rating Based Modeling of Credit Risk the authors develop a much more sophisticated analysis of migration behavior. Their contribution of more sophisticated techniques to measure and forecast changes in migration behavior as well as determining adequate estimators for transition matrices is a major contribution to rating based credit modeling. Internal ratings-based systems are widely used in banks to calculate their value-at-risk (VAR) in order to determine their capital requirements for loan and bond portfolios under Basel II One aspect of these ratings systems is credit migrations, addressed in a systematic and comprehensive way for the first time in this book The book is based on in-depth work by Trueck and Rachev
Author : Yong Zeng,Shu Wu
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 48,7 Mb
Release : 2013-08-15
Category : Business & Economics
ISBN : 9781461477891
State-space models as an important mathematical tool has been widely used in many different fields. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. The book includes nonlinear and non-Gaussian time series models, regime-switching and hidden Markov models, continuous- or discrete-time state processes, and models of equally-spaced or irregularly-spaced (discrete or continuous) observations. The contributed chapters are divided into four parts. The first part is on Particle Filtering and Parameter Learning in Nonlinear State-Space Models. The second part focuses on the application of Linear State-Space Models in Macroeconomics and Finance. The third part deals with Hidden Markov Models, Regime Switching and Mathematical Finance and the fourth part is on Nonlinear State-Space Models for High Frequency Financial Data. The book will appeal to graduate students and researchers studying state-space modeling in economics, statistics, and mathematics, as well as to finance professionals.
Author : Claus Munk
Publisher : Oxford University Press
Page : 573 pages
File Size : 50,9 Mb
Release : 2011-06-30
Category : Business & Economics
ISBN : 9780199575084
A large number of securities related to various interest rates are traded in financial markets. Traders and analysts in the financial industry apply models based on economics, mathematics and probability theory to compute reasonable prices and risk measures for these securities. This book offers a unified presentation of such models and securities.
