Semi-Markov Migration Models for Credit Risk

The credit derivatives market is booming and, for the first time, expanding into the banking sector which previously has had very little exposure to quantitative modeling. This phenomenon has forced a large number of professionals to confront this issue for the first time. Credit Derivatives Pricing Models provides an extremely comprehensive overview of the most current areas in credit risk modeling as applied to the pricing of credit derivatives. As one of the first books to uniquely focus on pricing, this title is also an excellent complement to other books on the application of credit derivatives. Based on proven techniques that have been tested time and again, this comprehensive resource provides readers with the knowledge and guidance to effectively use credit derivatives pricing models. Filled with relevant examples that are applied to real-world pricing problems, Credit Derivatives Pricing Models paves a clear path for a better understanding of this complex issue. Dr. Philipp J. Sch?nbucher is a professor at the Swiss Federal Institute of Technology (ETH), Zurich, and has degrees in mathematics from Oxford University and a PhD in economics from Bonn University. He has taught various training courses organized by ICM and CIFT, and lectured at risk conferences for practitioners on credit derivatives pricing, credit risk modeling, and implementation.

This title considers the special of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times. The class of semi-Markov processes includes strong Markov processes, L?vy and Smith stepped semi-Markov processes, and some other subclasses. Extensive coverage is devoted to non-Markovian semi-Markov processes with continuous trajectories and, in particular, to semi-Markov diffusion processes. Readers looking to enrich their knowledge on Markov processes will find this book a valuable resource.

This book is an introductory guide to using L?vy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets – the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of L?vy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of L?vy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.

A practical guide to counterparty risk management and credit value adjustment from a leading credit practitioner Please note that this second edition of Counterparty Credit Risk and Credit Value Adjustment has now been superseded by an updated version entitled The XVA Challenge: Counterparty Credit Risk, Funding, Collateral and Capital. Since the collapse of Lehman Brothers and the resultant realization of extensive counterparty risk across the global financial markets, the subject of counterparty risk has become an unavoidable issue for every financial institution. This book explains the emergence of counterparty risk and how financial institutions are developing capabilities for valuing it. It also covers portfolio management and hedging of credit value adjustment, debit value adjustment, and wrong-way counterparty risks. In addition, the book addresses the design and benefits of central clearing, a recent development in attempts to control the rapid growth of counterparty risk. This uniquely practical resource serves as an invaluable guide for market practitioners, policy makers, academics, and students.

The first decade of the 21st Century has been disastrous for financial institutions, derivatives and risk management. Counterparty credit risk has become the key element of financial risk management, highlighted by the bankruptcy of the investment bank Lehman Brothers and failure of other high profile institutions such as Bear Sterns, AIG, Fannie Mae and Freddie Mac. The sudden realisation of extensive counterparty risks has severely compromised the health of global financial markets. Counterparty risk is now a key problem for all financial institutions. This book explains the emergence of counterparty risk during the recent credit crisis. The quantification of firm-wide credit exposure for trading desks and businesses is discussed alongside risk mitigation methods such as netting and collateral management (margining). Banks and other financial institutions have been recently developing their capabilities for pricing counterparty risk and these elements are considered in detail via a characterisation of credit value adjustment (CVA). The implications of an institution valuing their own default via debt value adjustment (DVA) are also considered at length. Hedging aspects, together with the associated instruments such as credit defaults swaps (CDSs) and contingent CDS (CCDS) are described in full. A key feature of the credit crisis has been the realisation of wrong-way risks illustrated by the failure of monoline insurance companies. Wrong-way counterparty risks are addressed in detail in relation to interest rate, foreign exchange, commodity and, in particular, credit derivative products. Portfolio counterparty risk is covered, together with the regulatory aspects as defined by the Basel II capital requirements. The management of counterparty risk within an institution is also discussed in detail. Finally, the design and benefits of central clearing, a recent development to attempt to control the rapid growth of counterparty risk, is considered. This book is unique in being practically focused but also covering the more technical aspects. It is an invaluable complete reference guide for any market practitioner with any responsibility or interest within the area of counterparty credit risk.

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.

This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.

Written by leading market risk academic, Professor Carol Alexander, Value-at-Risk Models forms part four of the Market Risk Analysis four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Parametric linear value at risk (VaR)models: normal, Student t and normal mixture and their expected tail loss (ETL); New formulae for VaR based on autocorrelated returns; Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR; Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas; Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios; Decomposition of systematic VaR of large portfolios into standard alone and marginal VaR components; Backtesting and the assessment of risk model risk; Hypothetical factor push and historical stress tests, and stress testing based on VaR and ETL.

A comprehensively updated and reorganized new edition. The updates include comparative methods for improving reliability; methods for optimal allocation of limited resources to achieve a maximum risk reduction; methods for improving reliability at no extra cost and building reliability networks for engineering systems. Includes: A unique set of 46 generic principles for reducing technical risk Monte Carlo simulation algorithms for improving reliability and reducing risk Methods for setting reliability requirements based on the cost of failure New reliability measures based on a minimal separation of random events on a time interval Overstress reliability integral for determining the time to failure caused by overstress failure modes A powerful equation for determining the probability of failure controlled by defects in loaded components with complex shape Comparative methods for improving reliability which do not require reliability data Optimal allocation of limited resources to achieve a maximum risk reduction Improving system reliability based solely on a permutation of interchangeable components