Credit: Corporate Bonds, Credit Spreads, and the Default Option

Everything in Topic 2 assumed that the issuer would pay every cash flow on time and in full. The moment that assumption is relaxed, the discount rate must compensate for default risk — and the bond's price becomes an option-like quantity: the bondholder effectively owns a risk-free bond and has sold the issuer a put option on the firm's assets (the default option).

This topic builds the conceptual infrastructure for credit risk in three steps:

First, the instruments. A corporate bond is a risk-free Treasury-like structure augmented with covenants, call provisions, and — above all — the possibility of default. Understanding the indenture, the capital structure hierarchy, and the rating system is prerequisite to pricing.

Second, the credit spread. The spread between a corporate bond's yield and a matched-maturity Treasury yield is the market's price for default risk. It responds to issuer creditworthiness, recovery-rate expectations, supply-demand conditions, and macroeconomic stress. The spread contains both the expected loss from default and a credit risk premium for bearing the uncertainty about when and how much.

Third, the quantitative framework. The hazard rate

\lambda

(instantaneous conditional default probability) and survival probability

e^{-\lambda t}

give a compact, analytically tractable model for credit risk. The credit triangle — spread

\approx \lambda(1-R)

, where

R

is the recovery rate — links the three observable/estimable quantities: spread, default intensity, and recovery.

By the end of this topic you should be able to:

describe the key features of a corporate bond indenture: covenants, call provisions, and the capital structure hierarchy;
map a credit rating to an investment-grade/high-yield classification and describe the rating lifecycle;
define the credit spread as the excess yield over the risk-free curve and explain its two components (expected loss + risk premium);
state the risky bond identity: risky bond = risk-free bond − default option;
define the hazard rate $\lambda$ , derive the survival probability $e^{-\lambda t}$ , and compute default probabilities over any horizon;
derive the credit triangle: spread $\approx \lambda(1-R)$ , and use it to estimate the hazard rate from an observed spread.

In this lesson

Contents
The big picture

The full lesson is for members.

Read the full lesson

New to SelfMadeQuant.com? See membership options or browse the Financial Instruments, Markets and Conventions syllabus.