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 Prof. Giovanni Battista Di Masi.
[10][11] 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.
Brigo has been the most cited author for the technical section of Risk Magazine in the twenty years periods 1998–2017,[5] and his research on credit-default-swaps (CDS)-calibration has been referenced in legal proceedings.
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.
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)[22] and the related entry.
Brigo focused also on multiname credit derivatives, showing in Brigo, Pallavicini and Torresetti (2007),[20] 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 financial crisis of 2007–2008.
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),[23] 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).
Brigo and co-authors were also among the first to introduce rigorously the debit valuation adjustment (DVA),[25] while a volume on the updated nonlinear theory of valuation, including credit effects,[6] collateral modeling and funding costs, has appeared in Brigo, Morini and Pallavicini (2013), a volume that also collects investigation of wrong way risk across asset classes[28] and collects earlier research of the authors on collateral modeling and funding costs.
[30] This research continued with Brigo, Buescu, and Rutkowski (2017), reconciling credit and funding effects with a basic option pricing theory,[29] Brigo, Francischello and Pallavicini (2019) for a fully rigorous analysis of valuation as a fully nonlinear problem expressed mathematically through backward stochastic differential equations and semi-linear partial differential equations,[25] and Brigo, Buescu, Francischello, Pallavicini and Rutkowski (2022) to reconcile the mathematically rigorous results on nonlinear valuation and valuation adjustments based on cash flows adjustments with an approach based on hedging.
Brigo and co-authors further approached mathematical finance in general from a pathwise point of view, trying to establish results independently of the probabilistic setting.
Armstrong, Bellani, Brigo and Cass (2021) show how to obtain option prices without probability theory, using rough paths techniques.
This interpretation is related to Schwartz morphism and was developed in Armstrong and Brigo (2018) via the structure of jet bundles, with applications to filtering for both ordinary and quantum systems.