Suppose the firm issues a single zero-coupon bond with time to maturity 3 years and maturity val

step 1 So, here in first part to compute the price of the bond, we can use the formula P is equals to F

Suppose the firm issues a single zero-coupon bond with time...

Key Concepts

Pricing of Bonds with Credit Risk

When pricing bonds subject to default risk, the expected cash flows must be adjusted to incorporate the probability of default as well as the potential recovery rate in the event of a default. The bond price is then computed as the discounted expected payoff, reflecting both the time value of money and the likelihood of receiving reduced payments if default occurs.

Zero Coupon Bond

A zero coupon bond is a debt security that does not pay periodic interest (coupons) but is issued at a discount to its face (or par) value. At maturity, the investor is paid the full face value. This instrument is fundamentally used in assessing the time value of money and for building yield curves, as its pricing directly reflects the market’s discount factors over time.

Yield to Maturity (YTM)

Yield to maturity is the internal rate of return earned by an investor if a bond is held until it matures, assuming all payments are made as scheduled. It summarises the total return of the bond, accounting for both the purchase price and the difference between the purchase price and the maturity (or par) value. Calculating YTM is important for comparing bonds with different characteristics such as price and term.

Default Probability

Default probability represents the likelihood that a borrower will fail to meet its debt obligations. In the context of bond pricing, this metric is essential for adjusting expected cash flows to account for the risk of non-payment. It plays a critical role in credit risk analysis and in determining the appropriate yield spread over risk-free rates.

Expected Recovery

Expected recovery, often expressed as a recovery rate, measures the amount that investors are expected to recover in the event of a default relative to the bond's face value. This parameter is used along with default probability to adjust the bond’s expected cash flows, thereby affecting its valuation and the computed yield to maturity.

Verification of Theoretical Equations

In credit-sensitive bond pricing, equations such as the one referenced (equation 26.5) relate the bond’s price, yield, default probability, and expected recovery. Verifying these relationships involves showing that the pricing formula balances out by equating the discounted expected cash flows to the bond’s market price under the assumed risk and recovery assumptions. This exercise highlights the consistency and applicability of theoretical models in practical situations.

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