Corporate Security Prices in Structural Credit Risk Models with Incomplete Information: Extended Version

TL;DR

This paper develops a framework for pricing and hedging derivatives in structural credit risk models with incomplete information, using stochastic filtering and SPDEs to handle unobservable asset values.

Contribution

It introduces a novel approach to incorporate incomplete information into structural credit risk models via filtering techniques and SPDEs, enabling more realistic derivative pricing.

Findings

Derived an SPDE-characterization for the filter density.

Characterized default intensity under incomplete information.

Demonstrated application to option pricing and hedging.

Abstract

The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to compute the price dynamics of traded securities one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and we apply results from the filtering literature to this problem. In this way we obtain an SPDE-characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and we determine the price dynamics of traded securities. Armed with these results we study derivative asset analysis in our setup: we explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study.