Pricing Credit-Risky Bonds with Credit Spreads

Summary

The note explains a basic approach to valuing a credit-risky bond: discount its promised principal and coupon payments using risk-free rates adjusted by a credit spread. This spread represents compensation for the issuer’s credit risk, so the valuation does not rely on risk-free discounting alone. The bond’s cash flows are discounted separately to their payment dates, with the adjusted rate incorporating both the risk-free curve and credit spread over the relevant period.

The answer says that a constant spread is often used when there is not enough market information to estimate how the spread varies over time. When prices or credit default swap data for the issuer are available, those observations may support estimating a term structure of credit spreads. The note offers a simplified valuation framework, but does not explain how to calibrate spreads, model default and recovery explicitly, or address differences among bond structures. Its usefulness therefore depends on the suitability of spread-based discounting for the instrument and available market data.

Key ideas

• Credit-risky bond cash flows can be discounted using risk-free rates adjusted by a credit spread.
• The principal and each coupon payment are discounted to their respective payment dates.
• A constant spread is a practical assumption when market data are insufficient to estimate a spread curve.
• Other issuer bonds or credit default swaps can provide information for estimating a term structure of spreads.

Tags

# Pricing credit risky bonds


# Pricing credit risky bonds












How do we price credit risky bonds?

If I discount the cash flows using LIBOR/zero rates, it won't take the credit riskiness into account. So should I use a rate based on the issuer's credit spread? Or is there a separate way to price in credit riskiness (maybe using default probabilities)?

## Answer by Brian B (score 2, accepted)

https://quant.stackexchange.com/a/9583

Normally, you do indeed add a credit spread $s$ to the risk-free spreads to price the bond. That is, if the coupons are $c_i$ at times $t_i$ and the notional is $Y$ then you price it as

$$ R\!B(t) =Y \exp{\left( -\int_t^T s(x)+r(x) dx \right) } +\sum_{i \ni t_i>t}^{N_c} c_i \exp{\left( -\int_t^{t_i} s(x)+r(x) dx \right) } $$

Normally you have too little information to incorporate a term structure for $s$, so you just make it some constant $s_0$. Once in a while you have enough information from other bonds or credit default swaps to determine a term structure.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.