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Implied Correlations Smiles Or Smirks Paper



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Implied Correlations Smiles or Smirks enay A ca George Washington University Deepak Agrawal Diversified Credit Investments Saiyid Islam Standard Poor s This version Aug 15 2007 Abstract With standardized collateralized debt obligation CDO tranches on credit default swap CDS indices trading very actively the concept of implied correlation and correlation trading have gained popularity in recent times In this paper we examine the commonly observed implied correlation smile pattern that is oftentimes interpreted to signal relative value opportunities across tranches We investigate whether implied correlation smile can arise as a result of model mis specifications in the industry standard one factor Gaussian copula default time model rather than relative mis pricing across tranches Our evidence shows that empirical features like fat tails in return distributions heterogeneous pair wise correlations heterogeneous spreads and correlation between default probabilities and recovery rates can give rise to smile patterns in implied correlations even when all the tranches are fairly priced The standard Gaussian copula model assumes away these features and is thus mis specified Our results suggest that implied correlations computed from this model are not very useful to determine relative mis pricing across tranches On the other hand we also show that one factor Gaussian copula model and implied correlations obtained from this model perform well for pricing a given tranche across time even in periods of market turmoil related to credit risk events JEL Classification G 12 G 13 Key words Collateralized Debt Obligations Gaussian Copula Implied Correlation Smile enay A ca is at George Washington University Department of Finance School of Business 2201 G Street NW Funger Hall Room 505 Washington DC 20052 Ph 202 994 9209 Fax 202 994 5017 Email sagca gwu edu Deepak Agrawal is at Diversified Credit Investments 201 Spear Street Suite 250 San Francisco CA 94105 Ph 415 321 7428 Email



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