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Credit risk
Modelling credit risk accurately is central to the practice of mathematical finance. This volume of the Mastering Mathematical Finance series offers a comprehensive and accessible introduction to the subject tailored specially for master's students. The book focuses on the two mainstream modelling approaches to credit risk, namely structural models and reduced form models, and on pricing selected credit risk derivatives. Balancing rigorous theory with real-world examples from the post-credit crisis financial markets, it takes readers through a natural development of mathematical ideas and financial intuition. Students, practitioners and researchers alike will benefit from the compact presentation and detailed worked examples, exercises and solutions.
Book
Review and Implementation of Credit Risk Models of the Financial Sector Assessment Program (FSAP)
The paper presents the basic Credit Risk+ model, and proposes some modifications. This model could be useful in the stress-testing financial sector assessments process as a benchmark for credit risk evaluations. First, we present the setting and basic definitions common to all the model specifications used in this paper. Then, we proceed from the simplest model based on Bernoulli-distributed default events and known default probabilities to the fully-fledged Credit Risk+ implementation. The latter is based on the Poisson approximation and uncertain default probabilities determined by mutually independent risk factors. As an extension we present a Credit Risk+ specification with correlated risk factors as in Giese (2003). Finally, we illustrate the characteristics and the results obtained from the different models using a specific portfolio of obligors.
eBook
Recent Advances in Credit Risk Modeling
As is well known, most models of credit risk have failed to measure the credit risks in the context of the global financial crisis. In this context, financial industry representatives, regulators and academics worldwide have given new impetus to efforts to improve credit risk modeling for countries, corporations, financial institutions, and financial instruments. The paper summarizes some of the recent advances in this regard. It considers modifications of structural models, including of the classical Merton model, and efforts to reconcile the structural and the reduced-form models. It also discusses the reassessment of the default correlations using copulas, the pricing of credit index options, and the determination of the prices of distressed debt and estimation of recovery values.
eBook
Semi-Markov migration models for credit risk
Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers.
Book
Counterparty credit risk, collateral and funding
\"The book's content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular 'concrete' financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a 'feel' for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered\"--provided by publisher.
eBook
Anticipating correlations
Financial markets respond to information virtually instantaneously. Each new piece of information influences the prices of assets and their correlations with each other, and as the system rapidly changes, so too do correlation forecasts. This fast-evolving environment presents econometricians with the challenge of forecasting dynamic correlations, which are essential inputs to risk measurement, portfolio allocation, derivative pricing, and many other critical financial activities. In Anticipating Correlations, Nobel Prize-winning economist Robert Engle introduces an important new method for estimating correlations for large systems of assets: Dynamic Conditional Correlation (DCC). Engle demonstrates the role of correlations in financial decision making, and addresses the economic underpinnings and theoretical properties of correlations and their relation to other measures of dependence. He compares DCC with other correlation estimators such as historical correlation, exponential smoothing, and multivariate GARCH, and he presents a range of important applications of DCC. Engle presents the asymmetric model and illustrates it using a multicountry equity and bond return model. He introduces the new FACTOR DCC model that blends factor models with the DCC to produce a model with the best features of both, and illustrates it using an array of U.S. large-cap equities. Engle shows how overinvestment in collateralized debt obligations, or CDOs, lies at the heart of the subprime mortgage crisis--and how the correlation models in this book could have foreseen the risks. A technical chapter of econometric results also is included.
eBook
Indifference pricing
This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. René Carmona brings together a who's who of leading experts in the field to provide the definitive introduction for students, scholars, and researchers. Until recently, financial mathematicians and engineers developed pricing and hedging procedures that assumed complete markets. But markets are generally incomplete, and it may be impossible to hedge against all sources of randomness.Indifference Pricingoffers cutting-edge procedures developed under more realistic market assumptions.
The book begins by introducing the concept of indifference pricing in the simplest possible models of discrete time and finite state spaces where duality theory can be exploited readily. It moves into a more technical discussion of utility indifference pricing for diffusion models, and then addresses problems of optimal design of derivatives by extending the indifference pricing paradigm beyond the realm of utility functions into the realm of dynamic risk measures. Focus then turns to the applications, including portfolio optimization, the pricing of defaultable securities, and weather and commodity derivatives. The book features original mathematical results and an extensive bibliography and indexes.
In addition to the editor, the contributors are Pauline Barrieu, Tomasz R. Bielecki, Nicole El Karoui, Robert J. Elliott, Said Hamadène, Vicky Henderson, David Hobson, Aytac Ilhan, Monique Jeanblanc, Mattias Jonsson, Anis Matoussi, Marek Musiela, Ronnie Sircar, John van der Hoek, and Thaleia Zariphopoulou.
The first book on utility indifference pricingExplains the fundamentals of indifference pricing, from simple models to the most technical onesGoes beyond utility functions to analyze optimal risk transfer and the theory of dynamic risk measuresCovers non-Markovian and partially observed models and applications to portfolio optimization, defaultable securities, static and quadratic hedging, weather derivatives, and commoditiesIncludes extensive bibliography and indexesProvides essential reading for PhD students, researchers, and professionals
eBook