Conditional survival probabilities under partial information: a recursive quantization approach with applications

TL;DR

This paper introduces a recursive quantization method to compute conditional survival probabilities in a realistic model where firm value is observed with noise, enabling better pricing of credit derivatives like CDS options.

Contribution

It develops a novel recursive quantization approach for approximating conditional default probabilities in models with noisy observations of firm value.

Findings

The method accurately approximates survival probabilities.

Error bounds for the approximation are established.

Numerical tests demonstrate the approach's effectiveness in pricing CDS options.

Abstract

We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers important challenges related to the computation of conditional default probabilities. In order to deal with general diffusions as firm value process, we derive a numerical procedure based on the recursive quantization method to approximate it. Then, we investigate the error approximation induced by our procedure. Eventually, numerical tests are performed to evaluate the performance of the method, and an application is proposed to the pricing of CDS options.