A Merton-Like Approach to Pricing Debt based on a non-Gaussian Asset Model

TL;DR

This paper extends Merton's credit risk model by incorporating non-Gaussian features such as fat tails and skewness into asset dynamics, improving the fit to observed credit spreads and aligning with empirical stock and option data.

Contribution

It introduces a generalized Merton-like model that accounts for non-Gaussian asset behavior, enhancing credit spread evaluation accuracy.

Findings

Model fits well to empirical credit spreads

Incorporates fat tails and skewness into asset modeling

Aligns with observed stock returns and option prices

Abstract

This paper is a contribution to the Proceedings of the Workshop Complexity, Metastability and Nonextensivity held in Erice 20-26 July 2004, to be published by World Scientific. We propose a generalization to Merton's model for evaluating credit spreads. In his original work, a company's assets were assumed to follow a log-normal process. We introduce fat tails and skew into this model, along the same lines as in the option pricing model of Borland and Bouchaud (2004, Quantitative Finance 4) and illustrate the effects of each component. Preliminary empirical results indicate that this model fits well to empirically observed credit spreads with a parameterization that also matched observed stock return distributions and option prices.