A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework

Burtschell, X; Gregory, Jonathan M.; Laurent, Jean Paul

doi:10.3905/jod.2009.16.4.009

Cited by 95 publications

(92 citation statements)

References 56 publications

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“…We refer to Burtschell et al (2009), Cousin and Laurent (2008a), Cousin and Laurent (2008c) or Gregory and Laurent (2008) for reviews of a number of popular pricing approaches. 4 For this reason, some authors have considered models, where the expected tranche loss surface is an input parameter.…”

Section: The Theory Is When You Know Everything and Nothing Work Thmentioning

confidence: 99%

“…36 Even though, looking in greater details, there are still a lot of rather arbitrary and often not noticed modelling choices. 37 See Cousin and Laurent (2008a), Cousin and Laurent (2008c) or Burtschell et al (2009) for reviews of such bottom-up models within a factor copula framework. The sensitivity approach applies to copulas models that, contrary to the base correlation approach, provide arbitrage-free CDO tranche quotes.…”

Section: Ii3 Delta Scatteringmentioning

confidence: 99%

“…Names cluster together according to the level of credit spreads and credit deltas are either equal to zero or one (see Burtschell et al (2009) for a detailed analysis). For instance, when looking at an equity tranche, the names with the highest credit spreads have a delta equal to one 38 , while the remaining names have a delta equal to zero.…”

Section: Ii3 Delta Scatteringmentioning

confidence: 99%

“…As a result, any payoff contingent to the dynamics of W ɶ up to time T can be described as a sum of stochastic integrals with respect to 1 , , n W W ɶ ɶ … . 15 At least when recovery rates are assumed to be deterministic. 16 Let us note however that the dynamics of CDO tranche prices is very difficult to make explicit in this framework since it involves the joint law of some correlated first passage times.…”

Section: I8 Hedging Credit Portfolio Derivatives In Multivariate Strmentioning

confidence: 99%

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Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Cousin¹,

Laurent

2011

Credit Risk Frontiers

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Section: The Theory Is When You Know Everything and Nothing Work Thmentioning

confidence: 99%

Section: Ii3 Delta Scatteringmentioning

confidence: 99%

Section: Ii3 Delta Scatteringmentioning

confidence: 99%

Section: I8 Hedging Credit Portfolio Derivatives In Multivariate Strmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Cousin¹,

Laurent

2011

Credit Risk Frontiers

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“…In Burtschell et al (2009) possible bounds on CDO tranche premiums are studied. In case of a comonotonic vector of default times a model-free lower bound on equity tranche premiums is provided, where model-free has to be understood with respect to the dependence structure between default dates.…”

Section: Applications Of the Theory Of Comonotonicity 41 Derivativesmentioning

confidence: 99%

Advanced Mathematical Methods for Finance

Nunno¹,

Øksendal²

2011

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Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview -without claiming to be complete -of the developments of the theory of comonotonicity and its applications, with an emphasis on the achievements over the last five years. These applications range from pricing and hedging of derivatives over risk management to life insurance. ComonotonicityOver the last two decades, researchers in economics, financial mathematics and actuarial science have introduced results related to the concept of comonotonicity in their respective fields of interest. In this paper, we give an overview of the relevant literature in these research fields, with the main emphasis on the development of the theory and its applications in finance and insurance over the last five years. Although it is our intention to give an extensive bibliographic overview, due to the high number of papers on applications of comonotonicity, it is impossible to present here an exhaustive overview of the recent literature. Further, we restrict this paper to a description of how and where comonotonicity comes in and refer to the relevant papers for a detailed mathematical description. In order to make this paper self-contained, we also provide a short overview of the basic definitions and initial main results of comonotonicity theory, hereby referring to part of the older literature on this topic.The concept of comonotonicity is closely related to the following well-known result, which is usually attributed to both Hoeffding (1940) and Fréchet (1951): For any n-dimensional random vector X ≡ (X 1 , X 2 , . . . , X n ) with multivariate cumulative distribution function (cdf) F X and marginal univariate cdf's F X 1 , F X 2 , . . . , F Xn and for any x ≡ (x 1 , x 2 , . . . , x n ) ∈ R n it holds that F X (x) ≤ min (F X 1 (x 1 ) , F X 2 (x 2 ) , . . . , F Xn (x n )) .(1)In the sequel, the notation R n (F X 1 , F X 2 , . . . , F Xn ) will be used to denote the class of all random vectors Y ≡ (Y 1 , Y 2 , . . . , Y n ) with marginals F Y i equal to the respective marginals F X i . The set R n (F X 1 , F X 2 , . . . , F Xn ) is called the Fréchet class related to the random vector X.The upper bound in (1) is reachable in the Fréchet class R n (F X 1 , F X 2 , . . . , F Xn ) in the sense that it is the cdf of an n-dimensional random vector with marginals given by F X i , i = 1, 2, . . . , n. * Department of Mathematics, ECARES, Université Libre de Bruxelles, CP 210, 1050 Brussels, Belgium † Faculty of Business and Economics, Katholieke Universiteit, 3000 Leuven, Belgium. ‡ Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000 Gent, Belgium 1 In order to prove the reachability property, consider a random variable U , uniformly distributed on the unit interval (0, 1). Then one has that F −1 X 1 (U ), F −1 X 2 (U ), . . . , F −1 Xn (U ) ∈ ...

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Factor Distributions Implied by Quoted CDO Spreads

Schlögl¹,

Schlögl²

2008

Frontiers in Quantitative Finance

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The rapid pace of innovation in the market for credit risk has given rise to a liquid market in synthetic collateralised debt obligation (CDO) tranches on standardised portfolios. To the extent that tranche spreads depend on default dependence between different obligors in the reference portfolio, quoted spreads can be seen as aggregating the market views on this dependence. In a manner reminiscent of the volatility smiles found in liquid option markets, practitioners speak of implied correlation "smiles" and "skews". We explore how this analogy can be taken a step further to extract implied factor distributions from the market quotes for synthetic CDO tranches.

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A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework

Cited by 95 publications

References 56 publications

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Advanced Mathematical Methods for Finance

Factor Distributions Implied by Quoted CDO Spreads

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