From the late nineties, the spectacular growth of a secondary market for credit through derivatives has been matched by the emergence of mathematical modeling analysing the credit risk embedded in these contracts. This book aims to provide a broad and deep overview of this modeling, covering statistical analysis and techniques, modeling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modeling, and securitization. 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 modeling, 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 modeling--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 securitization is covered, including house price modeling and pricing models for asset-backed CDOs.The current credit crisis has brought modeling 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 modeling that underpins both credit derivatives and securitization. Though technical in nature, the pros and cons of various approaches attempt to provide a balanced view of the role that mathematical modeling plays in the modern credit markets. This Handbook will appeal to students and researchers in statistics, economics, and finance, as well as practicioners, credit traders, and quantitative analysts.

The Oxford Handbook of Credit Derivatives (Oxford Handbooks)

Business & Money

Rennie, Andrew

Lipton, Alexander

Economics

Oxford University Press

<p>Here is the first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities. With mathematical precision and in a style tailored for market practioners, the authors describe key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model. Starting from discrete-time hedging on binary trees, the authors develop continuous-time stock models (including the Black-Scholes method). They stress practicalities including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. The authors provide a full glossary of probabilistic and financial terms.</p>

Financial Calculus: An Introduction to Derivative Pricing

Baxter, Martin

Cambridge University Press

Here is the first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities. With mathematical precision and in a style tailored for market practioners, the authors describe key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model. Starting from discrete-time hedging on binary trees, the authors develop continuous-time stock models (including the Black-Scholes method). They stress practicalities including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. The authors provide a full glossary of probabilistic and financial terms.

Science & Math

Mathematics

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