Dual Quantization for random walks with application to credit derivatives

TL;DR

This paper introduces a dual quantization algorithm for approximating inhomogeneous random walks, enhancing credit derivative valuation by providing second order error bounds and demonstrating superior numerical performance over existing methods.

Contribution

The paper presents a novel dual quantization approach with intrinsic stationarity for better approximation of inhomogeneous random walks in credit derivatives valuation.

Findings

Achieves second order error bounds for weak approximation.

Demonstrates improved numerical accuracy over saddlepoint and Stein's methods.

Effective in approximating conditional tranche functions of synthetic CDOs.

Abstract

We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which posses 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 in case of the approximation of the conditional tranche function of synthetic CDO products and draw comparisons to the approximations achieved by the saddlepoint method and Stein's method.