Dual quantization for random walks with application to credit derivatives

ABSTRACT We propose a new quantization algorithm for the approximation of inhomogeneous random walks, which are essential for the valuation of collateralized debt obligation (CDO) tranches in latent factor models. This approach is based on a dual quantization operator that shares an intrinsic stationarity and therefore automatically leads to a second-order error bound for the weak approximation. We illustrate the numerical performance of our methods for approximating the conditional tranche function of synthetic CDO products and draw comparisons to the approximations achieved by the saddlepoint method and Stein's method.