Using OAS, Duration, and Convexity to Compare Bonds
Summary
The discussion examines whether option-adjusted spread can support comparisons among bonds with embedded options, plain bonds, and floating-rate instruments, and whether a plain bond’s OAS matches its Z-spread. It also asks whether an OAS curve can help identify relative value among bonds from one issuer and seniority, and whether option-adjusted duration and convexity can be used in a second-order price approximation.
The response treats those comparisons and the approximation as theoretically possible, while stressing that their quality depends on the interest-rate model and its calibration. It cautions that OAS analysis may omit stochastic credit spreads and capital-structure changes, which can distort embedded-option valuation. For a bond with one call date, delta corresponds to risk-neutral exercise probability; for more complex call schedules, the response recommends obtaining exercise probabilities from the valuation model. These are qualified conceptual answers, not a worked comparison or empirical validation.
Key ideas
- OAS can place bonds with different option features on a common theoretical spread basis, subject to model quality.
- For a plain vanilla bond, the response says OAS and Z-spread coincide.
- OAS curves and option-adjusted duration and convexity can support relative-value and price-sensitivity analysis.
- Model calibration affects these results, and omitted stochastic credit spreads or capital-structure changes can limit them.
- For a single call date, delta represents risk-neutral exercise probability; more complex cases call for model-derived probabilities.
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Full text
# About Option Adjusted Spread, rate curves and bonds comparison
# About Option Adjusted Spread, rate curves and bonds comparison
I have few questions about using OAS as a measure of risk:
- does OAS allow for comparison between bonds with and without embedded options (e.g. a callable bond against a plain vanilla one against a floating rate one)?
- Is the OAS of plain vanilla bond equal to its Z-Spread?
- If 'yes', building an OAS curve to compare all issuer's bonds having same seniority is a correct way to seek cheap vs. expensive bonds?
- We know that $\frac{\Delta P}{P}\cong-\frac{D}{(1+y)}\Delta y+\frac{1}{2}C(\Delta y)^{2}$, where $D$ and $C$ are bond's Duration and Convexity, while $y$ stands for yield; if one uses Option Adjusted Duration/Convexity, is he allowed to use this second order approximation to estimate bond's price variation?
- If you have a callable bond, is Delta the risk neutral probability the issuer will call its bond?
Thanks,
## Answer by Brian B (score 5, accepted)
https://quant.stackexchange.com/a/4517
The answer to your first four questions is affirmative. Option-adjusting the spread makes an equivalence between everything theoretically possible, but the quality of results depends significantly on the quality of your interest rate model and its calibration. My personal opinion, though, is that the results need to be treated carefully because the OAS model does not (typically) include stochastic credit spreads and potential capital structure changes, and therefore tends to underprice the embedded options.
For a bond with a single call date, Delta would be the risk-neutral exercise probability, but that situation is nearly nonexistent. Since the interest rate model used for OAS can easily compute the exercise probability alongside valuation, you should just use the model to get it.
If you are not computing OAS yourself, you are probably working with pretty pathetic numbers because most commercial sources are poorly calibrated (I'm looking at you, Bloomberg).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.