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Article

Implied Correlations: Smiles or Smirks?

Senay Agca, Deepak Agrawal and Saiyid Islam
The Journal of Derivatives Winter 2008, 16 (2) 7-35; DOI: https://doi.org/10.3905/JOD.2008.16.2.007
Senay Agca
is an associate professorof finance at George Washington University in Washington, DC.
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  • For correspondence: sagca@gwu.edu
Deepak Agrawal
is director of quantitative research at Diversified Credit Investments in San Francisco, CA.
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  • For correspondence: dagrawal@dcinv.com
Saiyid Islam
is director of quantitative analytics and research at Standard & Poor’s in New York, NY.
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  • For correspondence: saiyid_islam@standardandpoors.com
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Abstract

Developing a pricing model for CDOs that can actually be implemented is a very challenging problem. In a credit portfolio with N obligors, there are N individual default probabilities, (N2 - N)/2 correlations, and N recovery rates, all of which are important determinants of the portfolio loss distribution. Fitting the default probabilities alone typically requires specifying probability distributions for the shared and idiosyncratic underlying factors. In light of all this complexity, the Gaussian copula model applied to a homogeneous portfolio has become the industry standard approach. But the shortcomings of this model in explaining market prices for CDO tranches are very visible in the strange, but consistent, v-shaped implied correlation skew. Agca, Agrawal, and Islam consider the many simplifying assumptions of the Gaussian copula model and explore the importance of each by weakening one at a time and studying how the correlation skew changes. Does allowing the common factor or the idiosyncratic factors to come from a fat-tailed distribution, rather than the normal, make a big difference? For the shared factor, yes, but for the idiosyncratic factor, no. How important is the assumption that all correlations are equal versus being distributed over a wide range as is the case when the correlations are estimated from the data? Neither seems to make much difference to the implied correlation skew. In the end, we learn which assumptions make the most difference in CDO pricing—even though the true source of the correlation skew remains elusive.

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Implied Correlations: Smiles or Smirks?
Senay Agca, Deepak Agrawal, Saiyid Islam
The Journal of Derivatives Nov 2008, 16 (2) 7-35; DOI: 10.3905/JOD.2008.16.2.007

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Implied Correlations: Smiles or Smirks?
Senay Agca, Deepak Agrawal, Saiyid Islam
The Journal of Derivatives Nov 2008, 16 (2) 7-35; DOI: 10.3905/JOD.2008.16.2.007
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    • IMPLIED VOLATILITY AND IMPLIED CORRELATION
    • STANDARD GAUSSIAN MODEL AND IMPLIED CORRELATIONS
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