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Double t Copula Pricing of Structured Credit Products: Practical aspects of a trustworthy implementation

by Frédéric D. Vrins of ING Wholesale Bank

February 2009

Abstract: In spite of its simplicity, the popular One Factor Gaussian Copula model remains the market standard for the valuation of CDO tranches and n-th to default. It suffers however from well-know weaknesses, mainly due to the tail behavior of the Normal distribution (namely: the tails are too light, and there is no tail dependence, whatever is the copula correlation). Alternative models have been proposed, among those is the double t copula, which does not share the Gaussian copula drawbacks while not being much more complex. In spite of its nice features, this framework suffers from some technical problems related to its implementation. Without a lot of care, this technique could easily lead to inconsistent results. In our opinion, these difficulties have prevent practitioners to really turn that theoretically sounding model into a workable pricing tool. This paper aims at filling this gap by giving routes toward a reliable implementation of the double t copula framework, throwing away the drawbacks of this framework compared to the Gaussian one.

The first purpose of this letter is to show that the implementation issues related to the double t model actually reduce to the estimation of integrals with respect to some student-t distributions. The second part of this note presents an efficient numerical method to perform this tedious task.

Keywords: Copula, CDO, NTD, Numerical Integration, Student-t, Gaussian Quadrature.

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