Recovering portfolio default intensities implied by CDO quotes
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.
|Date of creation:||03 Jan 2013|
|Publication status:||Published in Mathematical Finance, Wiley, 2013, 23 (1), pp.94-121. <10.1111/j.1467-9965.2011.00491.x>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00413730|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
- Stutzer, Michael, 1996. " A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
- Francis A. Longstaff & Arvind Rajan, 2008.
"An Empirical Analysis of the Pricing of Collateralized Debt Obligations,"
Journal of Finance,
American Finance Association, vol. 63(2), pages 529-563, 04.
- Francis A. Longstaff & Arvind Rajan, 2006. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," NBER Working Papers 12210, National Bureau of Economic Research, Inc.
- Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007.
"Common Failings: How Corporate Defaults Are Correlated,"
Journal of Finance,
American Finance Association, vol. 62(1), pages 93-117, 02.
- Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
- Jakob Sidenius & Vladimir Piterbarg & Leif Andersen, 2008. "A New Framework For Dynamic Credit Portfolio Loss Modelling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 163-197.
- Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276.
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