I have few questions about using OAS as a measure of risk:

  1. 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)?
  2. Is the OAS of plain vanilla bond equal to its Z-Spread?
  3. 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?
  4. 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?
  5. If you have a callable bond, is Delta the risk neutral probability the issuer will call its bond?



1 Answer 1


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).

  • $\begingroup$ Thank you for your answers, Brian B. Actually I'm using Bloomberg OAS, which uses Hull-White 1F model and does not provide much details about calibration. What's your opinion on using quasi-maximum likelihood method to infer stochastic processes parameters values? $\endgroup$
    – Lisa Ann
    Commented Nov 13, 2012 at 8:34
  • 2
    $\begingroup$ I'm not quite sure what quasi-maximum likelihood method is -- do you mean the generalized method of moments for time series? In that case I dislike it -- in principle the model should be calibrated to traded securities prices rather than history, because it is about prospective option pricing. $\endgroup$
    – Brian B
    Commented Nov 14, 2012 at 3:35
  • 1
    $\begingroup$ If you go to the Bloomberg OAS page, it does offer a few different OAS models, none of them great but you can get an idea of your potential model error that way. I think the help also reveals some detail about the calibration and if you pester the Bloomberg help desk enough they will have a quant get back to you with more complete details. $\endgroup$
    – Brian B
    Commented Nov 14, 2012 at 3:36

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