A Note on the Correlation Smile

Hager, Svenja; Schöbel, Rainer

doi:10.2139/ssrn.893041

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…Having a high number of defaults may make it more likely for "neighboring" firms to default. This phenomenon enables our model to correct the so-called "correlation smile" (e.g., Amato and Gyntelberg 2005;Hager and Schöbel 2006) in pricing CDOs, since a low probability for mezzanine level defaults naturally leads to lower spreads for the respective tranche. These will be illustrated in detail in Section 3.2.…”

Section: )mentioning

confidence: 93%

“…Recall that given a standard tranche on CDX.NA.IG, with given observed spread , and known , it is possible to “imply” the asset correlation parameter in . However, it is known (e.g., Amato and Gyntelberg 2005; Hager and Schöbel 2006) that implying in such a manner across all tranches results in a “smile”: The mezzanine tranche has lower implied correlation compared to the neighboring tranches. One plausible interpretation for this kind of smile is that the normal copula model underprices the senior tranches and overprices the equity tranche in comparison to the mezzanine tranche.…”

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confidence: 99%

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Graphical Models for Correlated Defaults

Filiz

Guo

Morton

et al. 2012

Mathematical Finance

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A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These techniques also provide a calibration algorithm based on maximum likelihood estimation. Finally, the model is compared with standard normal copula model in terms of tails of the loss distribution and implied correlation smile.

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Section: )mentioning

confidence: 93%

mentioning

confidence: 99%

Graphical Models for Correlated Defaults

Filiz

Guo

Morton

et al. 2012

Mathematical Finance

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“…It is intuitively clear that in general there can be more than one correlation matrix that leads to the respective tranche spreads s e , s m and s s . Hager and Schöbel [3] discuss this subject. Note that there might also be combinations of tranche spreads that can't be reproduced by any correlation matrix.…”

Section: The Optimization Problemmentioning

confidence: 99%

“…The dependence structure is chosen such that the resulting tranche prices are concordant with observed market prices or, respectively, such that the observed correlation smile is reproduced. Hager and Schöbel [3] showed that heterogeneous correlation structures are able to model a smile. After we derived a suitable asset correlation structure, we can use this dependency to price off-market products with the same underlying.…”

Section: Introductionmentioning

confidence: 99%

Deriving the Dependence Structure of Portfolio Credit Derivatives Using Evolutionary Algorithms

Hager

Schöbel

2006

Computational Science – ICCS 2006

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Abstract. The correct modeling of default dependence is essential for the valuation of portfolio credit derivatives. However, for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion there wouldn't be the implied correlation smile that is observed in the market. The purpose of this paper is to derive a correlation structure from observed CDO tranche spreads. The correlation structure is chosen such that all tranche spreads of the traded CDO can be reproduced. This implied correlation structure can then be used to price off-market tranches with the same underlying as the traded CDO. Using this approach we can significantly reduce the risk to misprice offmarket derivatives. Due to the complexity of the optimization problem we apply Evolutionary Algorithms.

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“…The dependence structure is chosen such that the resulting tranche prices are concordant with observed market prices or, respectively, such that the observed correlation smile is reproduced. Hager and Schöbel show in [3] that heterogeneous correlation structures are able to model a smile. After we derived a suitable asset correlation structure, we can use this dependency to price off-market products with the same underlying.…”

Section: Introductionmentioning

confidence: 99%