Short description:

Mathematical finance and financial engineering have been rapidly expanding fields of science over the past three decades. The main reason behind this phenomenon has been the success of sophisticated quantitative methodologies in helping professionals to manage financial risks. The newly developed credit derivatives industry has grown around the need to handle credit risk, which is one of the fundamental factors of financial risk. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better apprehending, modeling and hedging of this kind of risk. One of the objectives has been to understand links between credit risk and other major sources of uncertainty, such as the market risk or the liquidity risk. The main objective of this monograph is to present a comprehensive survey ofthe past developments in the area of credit risk research, as well as put forth the most recent advancements in this field. An important aspect of this text is that it attempts to bridge the gap between the mathematical theory of credit risk and the financial practice, which serves as the motivation for the mathematical modeling studied in the book. Mahtematical developments are presented in a thorough manner and cover the structural (value-of-the-firm) and the reduced-form (intensity-based) approaches to credit risk modeling, applied both to single and to multiple defaults. In particular, the book offers a detailed study of various arbitrage-free models of defaultable term structures with several rating grades. This book will serve as a valuable reference for financial analysts and traders involved with credit derivatives. Some aspects of the book may also be useful for market practitioners with managing credit-risk sensitives portfolios. Graduate students and researchers in areas such as finance theory, mathematical finance, financial engineering and probability theory will benefit from the book as well. On the technical side, readers are assumed to be familiar with graduate level probability theory, theory of stochastic processes, and elements of stochastic analysis and PDEs; some acquaintance with arbitrage pricing theory is also

Long description:

Mathematical finance and financial engineering have been rapidly expanding fields of science over the past three decades. The main reason behind this phenomenon has been the success of sophisticated quantitative methodolo­ gies in helping professionals manage financial risks. It is expected that the newly developed credit derivatives industry will also benefit from the use of advanced mathematics. This industry has grown around the need to handle credit risk, which is one of the fundamental factors of financial risk. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. Although in the first chapter we provide a brief overview of issues related to credit risk, our goal was to introduce the basic concepts and related no­ tation, rather than to describe the financial and economical aspects of this important sector of financial market. The interested reader may consult, for instance, Francis et al. (1999) or Nelken (1999) for a much more exhaustive description of the credit derivatives industry.

From the reviews:

T.R. Bielecki and M. Rutkowski

Credit Risk

Modeling, Valuation and Hedging

"A fairly complete overview of the most important recent developments of credit risk modelling from the viewpoint of mathematical finance . . . It provides an excellent treatment of mathematical aspects of credit risk and will also be useful as a reference for technical details to traders and analysts dealing with credit-risky assets. It is a worthwhile addition to the literature and will serve as highly recommended reading for students and researchers in the subject area for some years to come."

?MATHEMATICAL REVIEWS

"The main purpose of this outstanding monograph is to present a comprehensive survey of the existing developments in the area of credit risk research, as well as to put forth the most recent advancements in this field. An important feature of this book is its attempt to bridge the gap between the mathematical theory of credit risk and the financial practice. ... The content of this book provides an indispensable guide to graduate students, researchers, and also to advanced practitioners in the fields ... ." (Neculai Curteanu, Zentralblatt MATH, Vol. 979, 2002)

Table of Contents:

1. Introduction to Credit Risk.- 2. Corporate Debt.- 3. First-Passage-Time Models.- 4. Hazard Function of a Random Time.- 5. Hazard Process of a Random Time.- 6. Martingale Hazard Process.- 7. Case of Several Random Times.- 8. Intensity-Based Valuation of Defaultable Claims.- 9. Conditionally Independent Defaults.- 10. Dependent Defaults.- 11. Markov Chains.- 12. Markovian Models of Credit Migrations.- 13. Heath-Jarrow-Morton Type Models.- 14. Defaultable Market Rates.- 15. Modeling of Market Rates.- References.- Basic Notation.