Work out a bond's value and credit spread from assumed credit risk parameters
The idea
Value a risky bond by subtracting the credit valuation adjustment from its default-free value. Build a table by date: for each, loss given default is the exposure times (1 − recovery), the probability of default is, in this discrete-period approximation, the hazard rate times the probability of surviving to the start of the period (with a continuous hazard it would be survival to the start times 1 minus exp(-hazard x period length)), and expected loss is their product, discounted at the risk-free rate. The sum of the discounted expected losses is the CVA, so the bond's fair value is V = default-free value − CVA. The credit spread is the yield to maturity at that fair value less the risk-free yield. A quick check is that the spread is close to the hazard rate × (1 − recovery rate).
Formulas
Credit spread, approximately
credit spread ≈ POD × (1 − recovery rate)
- credit spread
- the yield over the risk-free rate that compensates for default
- POD
- the annual probability of default
- recovery rate
- the share of the exposure recovered after default
An approximation, using the annual expected loss. It ignores the liquidity and risk premiums that make observed spreads wider than expected loss alone, which is why real spreads rarely match it.
In the app: 4 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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