Damiano Brigo (born Venice, Italy 1966) is a mathematician known for research in mathematical finance, filtering theory, stochastic analysis with differential geometry, probability theory and statistics, authoring more than 130 research publications and three monographs.Publications and citations page in Google Scholar From 2012 he serves as full professor with a chair in mathematical finance at the Department of Mathematics of Imperial College London, where he headed the Mathematical Finance group in 2012–2019.Finextra newsInstitutional page at Imperial College London He is also a well known quantitative finance researcher, manager and advisor in the industry.Campbell, Alexander (2011). The Risk-Free Myth. Risk Magazine 24(3), March 2011, London, page 80. His research has been cited and published also in mainstream industry publications, including Risk Magazine, where he has been the most cited author in the twenty years 1998–2017.Degrees of Influence, Risk Magazine, December 2018, pp. 129, Table B.Has Basel got its numbers wrong? The Banker, Financial Times Group weekly magazine, June 21, 2011.Basel risk limits will not curb rogue traders, The Banker, Financial Times Group weekly magazine, Bracken Column, May 1, 2018. He is often requested as a plenary or invited speaker both at academic and industry international events.Damiano Brigo's CV at imperial.ac.uk, accessed on 20 July 2023, Imperial College London Brigo's research has also been used in court as support for legal proceedings.Research Excellence Framework 2014: King's College London impact case for mathematical finance
Education and career Brigo studied for a laurea degree in mathematics at the University of Padua, where he graduated cum laude with a dissertation on the nonlinear filtering problem under the supervision of Giovanni Battista Di Masi.Recording of invited talk on stochastic differential equations as 2-jets, at 1 minute, 2016 London School of Economics Risk and Stochastics Conference, London.University of Padua Alumni Page (in Italian) Brigo continued his studies with a Ph.D. under the primary supervision of Bernard Hanzon at the Free University of Amsterdam, with periods under the supervision of Francois Le Gland at IRISA/INRIA in Rennes, France, with the oversight of Jan van Schuppen at CWI in Amsterdam, with a dissertation that introduced and studied the projection filters.Entry at the Mathematics Genealogy Project After his PhD, Brigo pursued a career in the financial industry with several subsequent roles, first as a quantitative analyst in Banca Intesa in Milan, then as head of credit models in Banca IMI in London, and finally as a managing director with Fitch Ratings in London. While in the industry, Brigo had been appointed as external fixed income professor at Bocconi University and as a visiting professor at the Department of Mathematics at Imperial College London. By then a well known researcher and manager in the financial industry, Brigo moved to a full time academic career, starting with the Gilbart Chair full professorship in Financial Mathematics at King's College London (2010–2012), where he headed the financial mathematics group. In 2012 Brigo moved to a full professor position at the Department of Mathematics of Imperial College London, where he headed the group in 2012-2019 and where he still serves as chair in mathematical finance, while continuing advisory work in the financial industry, serving in the academic advisory board of several financial institutions, and as director of two industry research institutes in two subsequent periods in 2012–2017, being often invited as a speaker both at academic events and at events organized by the industry, with seminars, talks, lectures, panels and training courses for international conferences, universities, mathematical institutes, financial institutions, central banks and regulators.
Both during his run in the industry and his current work in academia, Brigo has been publishing academic and industry research. His joint monograph on interest rate models with Fabio Mercurio, Brigo and Mercurio (2006)Skovmand D. and Verhofen, M. (2007). Book Review. Interest Rate Models - Theory and Practice, 2nd edition, Springer 2006. Fin Mkts Portfolio Mgmt (2007) 21:135–137, DOI 10.1007/s11408-006-0038-yDonev, C. (2007). Review of Interest Rate Models - Theory and Practice with smile, inflation and credit for the Mathematics Association of America has been cited more than 3000 times as per Google Scholar and has been widely adopted by academics and practitioners, the 2001 first edition being already considered a standard reference by reviewers. Brigo also authored press columns and articles for The Banker and Risk Magazine. Brigo has been the most cited author for the technical section of Risk Magazine in the twenty years periods 1998–2017, and his research on credit-default-swaps (CDS)-calibration has been referenced in legal proceedings. More in detail, in 2011 the court of law in Novara, Italy, retried a case of financial intermediation after the bankruptcy of Lehman. The judgement explanation refers to Brigo's research article on credit calibration, which was an early online preprint version of Brigo, Morini and Tarenghi (2011), using their first passage firm-value models AT1P and SBTV to calibrate Lehman's CDS data, following an earlier application to Parmalat data. The court sentence states that "... in a recent study two different mathematical models (AT1P and SBTV) have been applied to the CDS trend of Lehman, and this shows that, despite a worsening of the estimate, even from a mathematical point of view, based on the CDS patterns, the survival probability of Lehman, even near the default event, was still high."
Research on nonlinear filtering: projection filters Brigo started his research work with the development and study of the projection filters, during his Ph.D. with Bernard Hanzon and Francois Le Gland, published mainly in Brigo, Hanzon and Le Gland (1998, 1999). This initial version of projection filters was investigated by the Swedish Defense Research Agency. The projection filters are nonlinear filters based on the differential geometric approach to statistics, also related to information geometry. This work was part of Brigo's Ph.D. studies, appearing in his Ph.D. dissertation "Filtering by projection on the manifold of exponential densities".
Projection filters approximate the stochastic partial differential equation (SPDE) of the optimal nonlinear filter, evolving in an infinite dimensional space, with a finite dimensional stochastic differential equation obtained via projection of the SPDE on a chosen finite dimensional manifold of probability densities. Brigo and co-authors considered different types of optimality criteria and metrics, leading to a variety of projection filters (besides the initial references, see in particular Armstrong and Brigo (2016), and Armstrong, Brigo and Rossi Ferrucci (2021)). Projection filters have been applied to several areas, including navigation, ocean dynamics, quantum optics and quantum systems, estimation of fiber diameters, estimation of chaotic time series, change point detection and other areas, with the relevant references listed in the related projection filters page applications.
Research on mathematical finance Mathematical finance is the research area where Brigo has been most active and is most known, both in academia and industry, authoring three monographs and about one hundred academic and industry publications.
Interest rate derivatives models Brigo and co-authors published several research papers on interest rate modeling, culminating in the monograph Brigo and Mercurio (2006) where the theory and practice of interest rate modelling are developed, including inflation modeling, credit risk modeling, early treatment of credit valuation adjustments and calibration of models to market data. The monograph collects a good part of the earlier published research by the two authors and further co-authors.
Volatility smile modeling In volatility smile modelling, Brigo and co-authors have introduced stochastic differential equations that are consistent with dynamical mixture models, both in a univariate setting in Brigo and Mercurio (2002) and Brigo, Mercurio and Sartorelli (2003), among others, and in a multivariate setting, allowing for reconciling single assets and index volatility smiles or triangulation of FX rates smiles, in Brigo, Rapisarda and Sridi (2018) and Brigo, Pisani and Rapisarda (2021).Fengler, M. R. (2005), Semiparametric modeling of implied volatility, Springer Verlag, Berlin.Musiela, M., and Rutkowski, M. (2004), Martingale Methods in Financial Modelling, 2nd Edition, Springer Verlag, Berlin. These mixture dynamics models have been successfully applied to different asset classes, see the specific entry for further references.
Credit derivatives and dynamic loss models From 2002, Brigo contributed also to credit derivatives modeling and counterparty credit risk valuation. Brigo and co-authors worked extensively on credit default swap and credit default options in particular, both for single name default options in Brigo (2005), Brigo and Alfonsi (2005), Brigo and El-Bachir (2010),Damien Ackerer, Damir Filipović (2019). Linear credit risk models. Finance and Stochastics, 24 (1), pages 169-214, doi 10.1007/s00780-019-00409-zTomasz R. Bielecki, Areski Cousin, Stéphane Crépey and Alexander Herbertsson (2014). A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries. Communications in Statistics - Theory and Methods 43(7), doi: 10.1080/03610926.2013.844251 and for credit default index options in Brigo and Morini (2011),Manuel Ammann, Mathis Moerke (2022). Credit variance risk premiums. European Financial Management, doi: 10.1111/eufm.12394 showing how one could properly include a systemic default event in the valuation and clarifying the role of information in the valuation. Brigo was also among the first to publish a method for valuation of constant maturity credit default swaps, a form of credit default swaps where the premium leg does not pay a fixed and pre-agreed amount but a floating spread from a reference vanilla CDS over a constant time to maturity, see Brigo (2006)Anlong Li (2006). Valuation of Swaps and Options on Constant Maturity CDS Spreads. Barclays Capital Research. Related 2006 SSRN Preprint available here. and the related entry. Brigo focused also on multiname credit derivatives, showing in Brigo, Pallavicini and Torresetti (2007), through a dynamic loss model, how data implied a 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 2008 financial crisis. This research has been updated in 2010, leading to the monograph Credit Models and the Crisis: A journey into CDOs, Copulas, Correlations and Dynamic Models by Brigo, Pallavicini and Torresetti (2010),Galina Andreeva, Jake Ansell and Tina Harrison (2014). Governance and Accountability of Public Risk. Financial Accountability and Management 30(3), pages 342-361, doi: 10.1111/faam.12036 where, besides the dynamic loss models, the authors show research published before the crisis in 2006, highlighting the problems of the implied and base correlation paradigms that were dominating the valuation of credit index tranches at the time, based on the Gaussian copula, including the impossibility to match specific tranche spread patterns and the issue of allowing for negative expected tranched losses that pointed at possible arbitrage, see for example Torresetti, Brigo and Pallavicini (2006).Cui, Q., & Ma, Y. (2014). Pricing synthetic CDO with MGB2 distribution. Statistics and Its Interface, 7(3), 309-318. https://dx.doi.org/10.4310/SII.2014.v7.n3.a1
Valuation adjustments, XVA and nonlinear valuation