Pricing And Hedging Of Cdo Squared Tranches By Using A One Factor ...
Pricing and Hedging of CDO-squared tranches by using a one
factor L´evy model
Florence Guillaume∗
Philippe Jacobs†
Wim Schoutens‡
Abstract
Copula models have become the market standard for the pricing of CDO tranches. These
models present two main advantages: the dependence structure between default times can be
specified independently of the marginal credit curves and the pricing rests on a semi-analytical
method. These two advantages still hold in the case of CDO-squared tranche pricing. The aim
of the first part of this talk consists of an extension of the commonly used Gaussian copula
model to the class of L´
evy copula models. More particularly, it provides a comparison of the
exponential copula L´
evy model with the classical Gaussian copula model for the pricing of
CDO-squared tranches. Several approximations of the recursive approach are considered: a full
Monte Carlo approximation, a multivariate Normal approximation of the joint inner CDO loss
distribution firstly proposed by Shelton and a multivariate Poisson approximation of the joint
number of defaults affecting the inner CDOs. More particularly, a sensitivity analysis is carried
out for three particular days characterised by a low, medium and high value of the quoted
iTraxx and CDX index spreads. The second main part of this talk features a comparison of
the exponential L´
evy and Gaussian Deltas under the multivariate Normal approximation for a
period extended from the 20th of September 2007 until the 13rd of February 2008. The Deltas
are computed with respect to a weighted and unweighted versions of the CDS pool as well as
with respect to another CDO-squared tranche.
∗K.U.Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven, Belgium.
E-mail:
Florence.Guillaume@wis.kuleuven.be
†KBC, E-mail: philippe.jacobs@kbc.be
‡K.U.Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven, Belgium.
E-mail:
Wim.Schoutens@wis.kuleuven.be
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