Recovering portfolio default intensities implied by CDO quotes

Rama Cont () and Andreea Minca
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Rama Cont: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Andreea Minca: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We propose a stable non-parametric algorithm for the calibration of pricing models for portfolio credit derivatives: given a set of observations of market spreads for CDO tranches, we construct a risk-neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk neutral loss process 'closest' to a prior loss process, verifying the calibration constraints. We formalize the problem in terms of minimization of relative entropy with respect to the prior under calibration constraints and use convex duality methods to solve the problem: the dual problem is shown to be an intensity control problem, characterized in terms of a Hamilton--Jacobi system of differential equations, for which we present an analytical solution. We illustrate our method on ITRAXX index data: our results reveal strong evidence for the dependence of loss transitions rates on the past number of defaults, thus offering quantitative evidence for contagion effects in the risk--neutral loss process.

Keywords: intensity control; stochastic control; point process; inverse problem; nonparametric methods; credit risk; CDO; contagion (search for similar items in EconPapers)
Date: 2013-01-03
New Economics Papers: this item is included in nep-ban and nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-00413730
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Citations: View citations in EconPapers (8)

Published in Mathematical Finance, 2013, 23 (1), pp.94-121. ⟨10.1111/j.1467-9965.2011.00491.x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00413730

DOI: 10.1111/j.1467-9965.2011.00491.x

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