# Электронная книга: Damiano Brigo «Credit Models and the Crisis. A Journey into CDOs, Copulas, Correlations and Dynamic Models»

The recent financial crisis has highlighted the need for better valuation models and risk management procedures, better understanding of structured products, and has called into question the actions of many financial institutions. It has become commonplace to blame the inadequacy of credit risk models, claiming that the crisis was due to sophisticated and obscure products being traded, but practitioners have for a long time been aware of the dangers and limitations of credit models. It would seem that a lack of understanding of these models is the root cause of their failures but until now little analysis had been published on the subject and, when published, it had gained very limited attention. Credit Models and the Crisis is a succinct but technical analysis of the key aspects of the credit derivatives modeling problems, tracing the development (and flaws) of new quantitative methods for credit derivatives and CDOs up to and through the credit crisis. Responding to the immediate need for clarity in the market and academic research environments, this book follows the development of credit derivatives and CDOs at a technical level, analyzing the impact, strengths and weaknesses of methods ranging from the introduction of the Gaussian Copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. It also illustrates the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities, and explains why the Gaussian Copula model is still used in its base correlation formulation. The book reports both alarming pre-crisis research and market examples, as well as commentary through history, using data up to the end of 2009, making it an important addition to modern derivatives literature. With banks and regulators struggling to fully analyze at a technical level, many of the flaws in modern financial models, it will be indispensable for quantitative practitioners and academics who want to develop stable and functional models in the future. Издательство: "John Wiley&Sons Limited (USD)"
ISBN: 9780470667156 электронная книга Купить за 3902.37 руб и скачать на Litres |

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## Damiano Brigo

**Damiano Brigo** (Venice Italy 1966) is an applied mathematician, and current Gilbart Chair of Financial Mathematics at King's College, London, known for a number of results in systems theory, probability and mathematical finance.

## Contents |

## Main results

Brigo started his work with the development, with Bernard Hanzon and Francois Le Gland (1998), of the projection filters, a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry. With Fabio Mercurio (2002–2003), he has shown how to construct stochastic differential equations consistent with mixture models, applying this to volatility smile modeling in the context of local volatility models. With Aurelien Alfonsi (2005), Brigo introduced new families of multivariate distributions in statistics through the periodic copula function concept. Since 2002, Brigo contributed to credit derivatives modeling and counterparty risk, showing with Pallavicini and Torresetti (2007) how data implied non-negligible probability that several names defaulted together, showing some large default clusters and a concrete risk of high losses in collateralized debt obligations prior to the financial crisis of 2007–2008. This work has been further updated in 2010 leading to a volume for Wiley. Overall Brigo authored more than forty publications and co-authored the book *Interest rate models: theory and practice* for Springer-Verlag, that quickly became an international reference for stochastic dynamic interest rate modeling in finance.

## Current and past affiliations

Brigo is currently Managing Director at Fitch Solutions in London. Brigo has also been fixed income professor at the Bocconi University of Milan. He is currently the Gilbart Chair of Financial Mathematics at King's College, London, Visiting Professor at the Department of Mathematics of Imperial College and adjunct professor at the University of Essex. Brigo is also Managing Editor of the International Journal of Theoretical and Applied Finance for World Scientific. Brigo holds a PhD in Mathematics from the Free University of Amsterdam.

## Selected publications

- Brigo, D, Pallavicini, A, and Torresetti, R, Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Moels. Wiley, 2010.

- Brigo, D, Mercurio, F, Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit, Heidelberg, Springer Verlag, 2001, 2nd Edition 2006.

- Brigo, D, Hanzon, B, LeGland, F, A differential geometric approach to nonlinear filtering: The projection filter, IEEE T AUTOMAT CONTR, 1998, Vol: 43, Pages: 247 - 252, ISSN: 0018-9286

- Brigo, D, Hanzon, B, Le Gland, F, Approximate nonlinear filtering by projection on exponential manifolds of densities, BERNOULLI, 1999, Vol: 5, Pages: 495 - 534, ISSN: 1350-7265

- Brigo, D, On SDEs with marginal laws evolving in finite-dimensional exponential families, STAT PROBABIL LETT, 2000, Vol: 49, Pages: 127 - 134, ISSN: 0167-7152

- Brigo, D, Diffusion Processes, Manifolds of Exponential Densities, and Nonlinear Filtering, In: Ole E. Barndorff-Nielsen and Eva B. Vedel Jensen, editor, Geometry in Present Day Science, World Scientific, 1999

- Brigo, D, Mercurio, F, Lognormal-mixture dynamics and calibration to market volatility smiles, International Journal of Theoretical and Applied Finance, 2002, Vol: 5, Pages: 427 - 446

- Brigo, D, Mercurio, F, Sartorelli, G, Alternative asset-price dynamics and volatility smile, QUANT FINANC, 2003, Vol: 3, Pages: 173 - 183, ISSN: 1469-7688

- Alfonsi, A, Brigo, D, New families of copulas based on periodic functions, COMMUN STAT-THEOR M, 2005, Vol: 34, Pages: 1437 - 1447, ISSN: 0361-0926

- Brigo, D, Alfonsi, A, Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model, FINANC STOCH, 2005, Vol: 9, Pages: 29 - 42, ISSN: 0949-2984

- Brigo, D (2008), CDS Options through Candidate Market Models and the CDS-Calibrated CIR++ Stochastic Intensity Model, In: Wagner, N., editor, Credit Risk: Models, Derivatives and Management, Taylor & Francis, 2008

- Brigo, D, Pallavicini, A, Torresetti, R, (2007) Cluster-based extension of the generalized poisson loss dynamics andconsistency with single names, International Journal of Theoretical and Applied Finance, Vol: 10

- Brigo, D., Pallavicini, A. (2007). Counterparty Risk under Correlation between Default and Interest Rates. In: Miller, J., Edelman, D., and Appleby, J. (Editors), Numerical Methods for Finance, Chapman Hall.

## External links

- 21st-century mathematicians
- Financial economists
- Control theorists
- Researchers in stochastics
- Living people

Источник: Damiano Brigo

### См. также в других словарях:

**Late-2000s financial crisis**— The TED spread (in red) increased significantly during the financial crisis, reflecting an increase in perceived credit risk … Wikipedia**Copula (probability theory)**— In probability theory and statistics, a copula can be used to describe the dependence between random variables. Copulas derive their name from linguistics. The cumulative distribution function of a random vector can be written in terms of… … Wikipedia**Damiano Brigo**— (Venice Italy 1966) is an applied mathematician, and current Gilbart Chair of Financial Mathematics at King s College, London, known for a number of results in systems theory, probability and mathematical finance. Contents 1 Main results 2… … Wikipedia