Contrast the Z-spread with the option-adjusted spread
The idea
The Z-spread is the constant amount added to every point on the benchmark spot curve that makes the present value of a bond's cash flows equal its price. Because it is applied across the whole curve, it accounts for curve shape in a way the I-spread does not. The option-adjusted spread takes the Z-spread and removes the value of any embedded option, using an interest rate model. For a callable bond the option benefits the issuer, so the option-adjusted spread is below the Z-spread; for a putable bond it is above. Of these spreads, the option-adjusted spread is the one comparable across bonds with different option features.
A practice question
What is the Z-spread?
- The spread over the benchmark yield at the bond's maturityWhy not: That is the I-spread, a single-point comparison. The Z-spread is exactly what fixes that limitation.
- The constant spread added to every point on the spot curve that makes present value equal price — correct
- The difference between the bid and ask yieldsWhy not: A transaction cost, not a valuation measure.
Applying the spread at every maturity rather than at one point is what makes it account for the shape of the curve.
A harder one
For a putable bond, how does the option-adjusted spread compare with the Z-spread?
- It is lowerWhy not: That is the callable case, where the holder has written the option. A put is owned by the holder, so removing its value leaves more spread.
- It is equalWhy not: They coincide only when there is no embedded option to value.
- It is higher — correct
The put benefits the holder, so removing its value leaves more spread than the raw measure showed.
The hardest tier
Two desks publish different option-adjusted spreads for the same bond on the same day. How?
- One of them has made an arithmetic errorWhy not: Both can be computed correctly. The inputs differ, not the arithmetic.
- They assumed different rate volatility — correct
- They are quoting on different day count conventionsWhy not: Conventions would produce a trivial difference, and both desks would use the market standard for the instrument.
The embedded option is valued differently as a result. The measure depends on a model, which is the price paid for a number that is comparable across option features.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →