Generalizing Merton's approach of pricing risky debt: some closed form results

TL;DR

This paper extends Merton's model for pricing risky debt by incorporating the CIR interest rate model with non-zero correlation, providing new closed-form solutions for more realistic financial scenarios.

Contribution

It generalizes Merton's approach to include non-zero correlation between firm value and interest rates, deriving new closed-form pricing formulas.

Findings

Closed-form solutions for non-zero correlation cases.

Extension of previous models to more realistic interest rate dynamics.

Analytical results applicable to risk management and pricing.

Abstract

In this work, I generalize Merton's approach of pricing risky debt to the case where the interest rate risk is modeled by the CIR term structure. Closed form result for pricing the debt is given for the case where the firm value has non-zero correlation with the interest rate. This extends previous closed form pricing formular of zero-correlation case to the generic one of non-zero correlation between the firm value and the interest rate.