Explaining the Levy base correlation smile

Joao Garcia and Serge Goossens look at base expected loss at maturity both in the Gaussian copula and Levy-based models, and link it to base correlation in these frameworks. They report on the existence of smile in both base correlation curves and discuss different interpolation methodologies in the absence of arbitrage. Finally, they discuss the properties of these curves for tranchlet pricing purposes and for correlation mapping for bespoke portfolios

Since the introduction of the one-factor Gaussian copula model for pricing synthetic collateralised debt obligation (CDO) tranches by Andersen, Sidenius & Basu (2003), correlation has been seen as an exogenous parameter used to match observed market quotes. First the market adopted the concept of implied compound correlation. One of the problems of this approach is its unsuitability for interpolation. The current widespread market approach is to use the concept of base correlation introduced by

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