Explaining the Levy base correlation smile

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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