Damiano Brigo
Encyclopedia
Damiano Brigo 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
.
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 model
s, 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.
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.
Systems theory
Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...
, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and mathematical finance
Mathematical finance
Mathematical finance is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive and extend the mathematical...
.
Main results
Brigo started his work with the development, with Bernard HanzonBernard Hanzon
Bernand Hanzon is an academic, mathematician, and researcher. He has worked on systems theory, probability and statistics, and mathematical finance...
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
Information geometry
Information geometry is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory. It derives its name from the fact that the Fisher information is used as the Riemannian metric when considering the geometry of probability distribution families...
. With Fabio Mercurio
Fabio Mercurio
Fabio Mercurio is an Italian mathematician, internationally known for a number of results in mathematical finance.-Main results:...
(2002–2003), he has shown how to construct stochastic differential equations consistent with mixture model
Mixture model
In statistics, a mixture model is a probabilistic model for representing the presence of sub-populations within an overall population, without requiring that an observed data-set should identify the sub-population to which an individual observation belongs...
s, applying this to volatility smile
Volatility Smile
In finance, the volatility smile is a long-observed pattern in which at-the-money options tend to have lower implied volatilities than in- or out-of-the-money options. The pattern displays different characteristics for different markets and results from the probability of extreme moves...
modeling in the context of local volatility
Local volatility
A local volatility model, in mathematical finance and financial engineering, is one which treats volatility as a function of the current asset level S_t and of time t .-Formulation:...
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 UniversityBocconi University
Bocconi University is a private university located in central Milan, beside Parco Ravizza. Bocconi provides undergraduate, graduate and post-graduate education, in addition to a range of double degree programs, in the fields of economics, management, finance and law. According to many 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
World Scientific
World Scientific Publishing is a publisher of scientific, technical, and medical books and journals. The company was founded in 1981 and now employs more than 200 staff at its headquarters in Singapore, with offices worldwide in New Jersey, California, London, New Delhi, Tianjin, Sydney, Hong...
.
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 FinanceInternational Journal of Theoretical and Applied FinanceThe International Journal of Theoretical and Applied Finance was founded in 1998 and is published by World Scientific. It covers the use of quantitative tools in finance, including articles on development and simulation of mathematical models, their industrial usage, and application of modern...
, 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.