139 results found
Brigo D, Armstrong J, 2013, Stochastic filtering by projection: the example of the cubic sensor, Geometric Science of Information: First International Conference, Pages: 685-692
The “projection method” is an approach to finding numerical approximations to the optimal filter for non linear stochastic filtering problems. One uses a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic differential equation given by the filtering problem onto a finite dimensional manifold inside the space of densities. This reduces the problem to finite dimensional stochastic differential equation.Previously, the projection method has only been considered for the Hilbert space structure associated with the Hellinger metric. We show through the numerical example of the quadratic sensor that the approach also works well when one projects using the direct L 2 metric.Previous implementations of projection methods have been limited to solving a single problem. We indicate how one can build a computational framework for applying the projection method more generally.
Brigo D, Morini M, Pallavicini A, 2013, Counterparty Credit Risk, Collateral and Funding: with Pricing Cases for all Asset Classes, Publisher: Wiley, ISBN: 978-0-470-74846-6
The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.
BRIGO DAMIANO, CAPPONI AGOSTINO, PALLAVICINI ANDREA, et al., 2013, PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK, International Journal of Theoretical and Applied Finance, Vol: 16, Pages: 1350007-1350007, ISSN: 0219-0249
BRIGO DAMIANO, BUESCU CRISTIN, MORINI MASSIMO, 2012, COUNTERPARTY RISK PRICING: IMPACT OF CLOSEOUT AND FIRST-TO-DEFAULT TIMES, International Journal of Theoretical and Applied Finance, Vol: 15, Pages: 1250039-1250039, ISSN: 0219-0249
Brigo D, Capproni A, 2012, Bilateral Credit Valuation Adjustment with Application to Credit Default Swaps, Managing and Measuring Capital: For Banks and Financial Institutions, Editors: Ong, Publisher: Risk Books
Bielecki T, Brigo D, Patras F, 2011, Credit Risk Frontiers, Publisher: Bloomberg Press, ISBN: 9781576603581
This book addresses these aspects of modeling and analysis of credit derivatives that have not been adequately studied and/or adequately understood in the past.
Brigo D, Morini M, 2011, NO-ARMAGEDDON MEASURE FOR ARBITRAGE-FREE PRICING OF INDEX OPTIONS IN A CREDIT CRISIS, Mathematical Finance, Pages: 573-593
In this work, we consider three problems of the standard market approach to credit index options pricing: the definition of the index spread is not valid in general, the considered payoff leads to a pricing which is not always defined, and the candidate numeraire for defining a pricing measure is not strictly positive, which leads to a nonequivalent pricing measure. We give a solution to the three problems, based on modeling the flow of information through a suitable subfiltration. With this we consistently take into account the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show on market inputs that, while the pricing difference can be negligible in normal market conditions, it can become highly relevant in stressed market conditions, like the situation caused by the credit crunch.
Brigo D, Pallavicini A, Torresetti R, 2010, Credit models and the crisis : a journey into CDOs, copulas, correlations and dynamic models., Publisher: Wiley, ISBN: 978-0-470-66566-4
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 ...
Brigo D, El-Bachir N, 2010, An exact formula for default swaptions pricing in the SSRJD stochastic intensity model, Mathematical Finance, Vol: 20, Pages: 365-382
Ben-Ameur H, Brigo D, Errais E, 2009, A dynamic programming approach for pricing CDS and CDS options, QUANTITATIVE FINANCE, Vol: 9, Pages: 717-726, ISSN: 1469-7688
Ben Ameur H, Brigo D, Errais E, 2009, Pricing Credit Default Swaps Bermudan Options: An Approximate Dynamic Programming Approach, Quantitative Finance
Brigo D, Mercurio F, Rapisarda F, 2008, Smile at Uncertainty, Risk Magazine
Brigo D, Pallavicini A, 2008, Counterparty Risk under Correlation between Default and Interest Rates, Numercial Methods for Finance, Editors: Miller J, Edelman D, Appleby J, Publisher: Chapman Hall
Brigo D, Pallavicini A, 2008, Counterparty Risk and Contingent CDS under correlation, Risk Magazine
Brigo D, 2008, CDS Options through Candidate Market Models and the CDS-Calibrated CIR++ Stochastic Intensity Model, Credit Risk: Models, Derivatives and Management, Editors: Wagner, Publisher: Taylor & Francis
Brigo D, Pallavicini A, Torresetti R, 2007, Cluster-based extension of the generalized poisson loss dynamics and consistency with single names, International Journal of Theoretical and Applied Finance, Vol: 10, ISSN: 0219-0249
We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil  to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard "bottom-up" approaches, and to achieve true consistency with single names, improving on most "top-down" loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo et al. , which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.
Brigo D, Pallavicini A, Torresetti R, 2007, CDO calibration with the dynamical Generalized Poisson Loss model, Risk Magazine
Brigo D, Pallavicini A, Torresetti R, 2007, Cluster-based extension of the generalized poisson loss dynamics and consistency with single names, Credit Correlation - Life After Copulas, Editors: Lipton A, Rennie A, Publisher: World Scientific
Brigo D, 2006, Constant Maturity CDS valuation with market models, Risk Magazine
Brigo D, Morini M, 2006, Structural credit calibration, Risk Magazine
Brigo D, Mercurio F, 2006, Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit, Heidelberg, Publisher: Springer Verlag
Brigo D, Cousot L, 2006, A Comparison between the SSRD Model and the Market Model for CDS Options Pricing, International Journal of Theoretical and Applied Finance, Vol: 9
Brigo D, Masetti M, 2006, Risk Neutral Pricing of Counterparty Risk, Counterparty Credit Risk Modeling: Risk Management, Pricing and Regulation, Editors: Pykhtin, Publisher: Risk Books
Brigo D, Morini M, 2006, Efficient Analytical Cascade Calibration of the LIBOR market model with Endogenous Interpolation, Journal of Derivatives
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