CFA Level IFixed IncomeHard
A callable corporate bond has a Z-spread of 150 basis points over the benchmark spot curve and an option-adjusted spread (OAS) of 110 basis points. Based on this information, the value of the embedded call option, expressed as a spread, is closest to:
- A260 bp
- B110 bp
- C40 bp
- D150 bp
Show answer & explanationAnswer & explanation
Correct answer: C. 40 bp
For a callable bond, OAS = Z-spread − option cost, because the call option benefits the issuer at the bondholder's expense. Rearranging, option cost = Z-spread − OAS = 150 bp − 110 bp = 40 bp.
Why the other options are wrong
- A. Incorrectly sums rather than subtracts the two spreads.
- B. This is the OAS itself, not the option's value.
- D. This is the Z-spread itself, not the option's value.
OAS vs. Z-Spread (Option Cost)
The option-adjusted spread removes the value of an embedded option from the Z-spread, isolating pure credit/liquidity compensation; the difference reflects the option's cost.
- Callable bond: OAS < Z-spread (option costs the bondholder)
- Putable bond: OAS > Z-spread (option benefits the bondholder)
- Option cost (bp) = Z-spread − OAS for callable bonds
Memory trick: 'Z-spread minus OAS unmasks what the call option is costing you'