Modeling credit risk with mixed fractional Brownian motion: An application to barrier options

Abstract

This article aims to examine the pricing of debt and equity in the context of credit risk structural models, where the value of a company’s assets is influenced by mixed fractional Brownian motion. Three distinct scenarios are analyzed, including when the assets are trade-able, fixed, and subject to partial recovery of debt. The study culminates with the evaluation of debt pricing under the barrier model, where a bankruptcy threshold is established for the company’s asset value.

Keywords

• credit structural model
• mixed fractional brownian motion
• barrier option