A unified approach to pricing and risk management of equity and credit risk

TL;DR

This paper introduces a unified, analytically tractable framework for modeling equity and credit risks, integrating default time, stock price dynamics, and stochastic volatility through an affine process, enabling efficient pricing and risk management.

Contribution

It develops a novel affine-based model that jointly captures equity and credit risks, including a jump-to-default extension of the Heston model, with a comprehensive characterization of risk-neutral measures.

Findings

Model maintains analytical tractability.

Allows flexible interaction between risk factors.

Enables efficient risk management and pricing.

Abstract

We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intensity, while maintaining full analytical tractability. We characterise all risk-neutral measures which preserve the affine structure of the model and show that risk management as well as pricing problems can be dealt with efficiently by shifting to suitable survival measures. As an example, we consider a jump-to-default extension of the Heston stochastic volatility model.