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Credit models and the crisis: An overview
Journal of Risk Management in Financial Institutions,
4
(3),
243-253
(2011)
Abstract
This paper describes the evolution of methodologies used to price credit derivatives and collateralised debt obligations (CDOs): 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; and to the generalised Poisson loss (GPL) model in particular. The paper also discusses: (i) the implied copula model, which can consistently account for CDOs with different attachment and detachment points for a single maturity, and (ii) the notion of expected tranche loss, a model independent quantity that can be easily stripped from CDO data and may be useful for interpolation. The paper also notes that authors had raised objections to using Gaussian copulas and implied correlation in CDO modelling as far back as 2006, showing that the quantitative community was aware of these limitations before the crisis. The authors also comment here on why the Gaussian copulas are still used to model CDOs. Overall, they conclude that more work needs to be done to improve the modelling of CDOs and credit derivatives.
Keywords: credit derivatives; Gaussian copula model; implied correlation; base correlation; implied copula; dynamic loss model; collateralised debt obligations; DJi-Traxx and CDX tranches; CDO tranche calibration
The full article is available to subscribers to the journal.
Author's Biography
Damiano Brigo obtained a PhD in stochastic filtering with differential geometry from the Free University of Amsterdam, following a BSc in mathematics from the University of Padua. Since July 2007, he has been Managing Director and Global Head of the Quantitative Innovation team at Fitch Solutions, London. He is also currently Visiting Professor at the Department of Mathematics at Imperial College, London. He is author of the book ‘Interest Rate Models: Theory and Practice’ (Springer-Verlag), and his academic and practitioner-oriented articles have been published in financial modelling, probability and systems theory journals. Damiano is Managing Editor of the International Journal of Theoretical and Applied Finance.
Andrea Pallavicini has a degree in astrophysics and a PhD in theoretical and mathematical physics from the University of Pavia. He is currently Head of Financial Engineering at Banca Leonardo in Milan. Over the years, he has written a number of academic and practitioner-oriented articles on financial modelling, theoretical physics and astrophysics. He has taught master’s courses in finance at the universities of Pavia and Milan. His main contributions in finance concern dynamical loss models, risk-neutral evaluation of counterparty risk, smile modelling in the swaption market, and pricing of exotic equity and/or interest-rate derivatives.
Roberto Torresetti is responsible for the synthetic structured credit derivatives business at BBVA. He was previously a senior credit derivatives modeller at Banca IMI and equity derivatives analyst at Lehman Brothers. He was also a quantitative fund manager at San Paolo IMI Asset Management. He holds a bachelor’s degree in economics from Università Bocconi in Milan and completed his MA in economics at Università Bocconi and MS in financial mathematics at the University of Chicago.
Citation
Brigo, Damiano, Pallavicini, Andrea and Torresetti, Roberto (2011, June 1). Credit models and the crisis: An overview. In the Journal of Risk Management in Financial Institutions, Volume 4, Issue 3. https://doi.org/10.69554/PAMZ2204.
© Henry Stewart
Publications LLP
Publications LLP