Recently, various semi-analytical methods have been developed to offer less time consuming alternatives to Monte Carlo simulation for the pricing of correlation credit derivatives products (like single tranche CDO and CDO squared). The motivation of this note is to present and compare these methods and suggests quantitative insights into their relative efficiency both in terms of accuracy and computing time. 

In particular, we compare the standard recursive method originally developped by Hull and White with a new bred method that can provide more accurate result and based on Fourier transformation. This method referred to as the polynomial generating function turns out to be very accurate and is used as a benchmark for our various methods.

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