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.

Rating Based Modeling of Credit Risk: Theory and Application of Migration Matrices (Academic Press Advanced Finance)

Business & Money

Rachev, Svetlozar T.

Trueck, Stefan

Economics

Academic Press

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.

Mass Transportation Problems: Applications (Probability and Its Applications)

Science & Math

Rüschendorf, Ludger

Mathematics

Springer

This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures

Fabozzi, Frank J.

Stoyanov, Stoyan V.

wiley

A comprehensive look at how probability and statistics is applied to the investment process 
Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before. In order to keep up, you need a firm understanding of this discipline. Probability and Statistics for Finance addresses this issue by showing you how to apply quantitative methods to portfolios, and in all matter of your practices, in a clear, concise manner. Informative and accessible, this guide starts off with the basics and builds to an intermediate level of mastery. • Outlines an array of topics in probability and statistics and how to apply them in the world of finance • Includes detailed discussions of descriptive statistics, basic probability theory, inductive statistics, and multivariate analysis • Offers real-world illustrations of the issues addressed throughout the text The authors cover a wide range of topics in this book, which can be used by all finance professionals as well as students aspiring to enter the field of finance.

Probability and Statistics for Finance

Focardi, Sergio M.

Hoechstoetter, Markus

Finance

An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management 
In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. <ul>
<li>Reviews the basics of probability distributions</li> <li>Analyzes a continuous time option pricing model (the so-called exponential Lévy model)</li> <li>Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods</li> <li>Studies two multivariate settings that are suitable to explain joint extreme events</li> </ul>
Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Financial Models with Levy Processes and Volatility Clustering

Kim, Young Shin

Bianchi, Michele L.

While operational risk has long been regarded as a mere part of "other" risks--outside the realm of credit and market risk--it has quickly made its way to the forefront of finance. In fact, with implementation of the Basel II Capital Accord already underway, many financial professionals--as well as those preparing to enter this field--must now become familiar with a variety of issues related to operational risk modeling and management. 
Written by the experienced team of Anna Chernobai, Svetlozar Rachev, and Frank Fabozzi, Operational Risk will introduce you to the key concepts associated with this discipline. Filled with in-depth insights, expert advice, and innovative research, this comprehensive guide not only presents you with an abundant amount of information regarding operational risk, but it also walks you through a wide array of examples that will solidify your understanding of the issues discussed. Topics covered include: <ul>
<li>The main challenges that exist in modeling operational risk.</li> <li>The variety of approaches used to model operational losses.</li> <li>Value-at-Risk and its role in quantifying and managing operational risk.</li> <li>The three pillars of the Basel II Capital Accord.</li> <li>And much more.</li> </ul>

Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis

Chernobai, Anna S.

A comprehensive guide to financial econometrics 
Financial econometrics is a quest for models that describe financial time series such as prices, returns, interest rates, and exchange rates. In Financial Econometrics, readers will be introduced to this growing discipline and the concepts and theories associated with it, including background material on probability theory and statistics. The experienced author team uses real-world data where possible and brings in the results of published research provided by investment banking firms and journals. Financial Econometrics clearly explains the techniques presented and provides illustrative examples for the topics discussed. Svetlozar T. Rachev, PhD (Karlsruhe, Germany) is currently Chair-Professor at the University of Karlsruhe. Stefan Mittnik, PhD (Munich, Germany) is Professor of Financial Econometrics at the University of Munich. Frank J. Fabozzi, PhD, CFA, CFP (New Hope, PA) is an adjunct professor of Finance at Yale University’s School of Management. Sergio M. Focardi (Paris, France) is a founding partner of the Paris-based consulting firm The Intertek Group. Teo Jasic, PhD, (Frankfurt, Germany) is a senior manager with a leading international management consultancy firm in Frankfurt.

Financial Econometrics: From Basics to Advanced Modeling Techniques

Mittnik, Stefan

Jašic, Teo

Bayesian Methods in Finance provides a detailed overview of the theory of Bayesian methods and explains their real-world applications to financial modeling. While the principles and concepts explained throughout the book can be used in financial modeling and decision making in general, the authors focus on portfolio management and market risk management―since these are the areas in finance where Bayesian methods have had the greatest penetration to date.

Bayesian Methods in Finance

Hsu, John S. J.

Bagasheva, Biliana S.

Concentrates on four specialized research directions as well as applications to different problems of probability theory. These include: description of the basic structure of p. metrics, analysis of the topologies in the space of probability measures generated by different types of p. metrics, characterization of the ideal metrics for the given problem and investigations of the main relationships between different types of p. metrics. The presentation here is given in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.

Probability Metrics and the Stability of Stochastic Models (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section)

The authors reconsider the problem of parametrically specifying distribution suitable for asset-return models. They describe alternative distributions, showing how they can be estimated and applied to stock-index and exchange-rate data. The implications for options pricing are also investigated.

Stable Paretian Models in Finance

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