How to Check a Bond’s Swap Curve and Z-Spread
Summary
A bond’s Z-spread is found by projecting its cash flows and shifting a reference swap curve in parallel until the discounted cash flows equal the bond’s dirty price. The note explains that this calculation depends on accurate bond terms and an appropriate curve, so a reported spread can be wrong even when the calculation itself is straightforward.
Possible errors include treating an amortizing bond as a bullet, using incorrect coupon or maturity data, or applying Z-spread to a callable bond whose option meaningfully affects its value. In that case, option-adjusted spread may be more suitable. The answer also cautions that the chosen swap curve matters: for short maturities, a curve based on swap rates may produce implausibly low or negative spreads, and a futures-based curve may be preferable. These are practical checks, not a full guide to curve construction or spread analytics; the answer also notes that a eurobond need not be denominated in euros.
Key ideas
- Z-spread equates a bond’s dirty price with the present value of projected cash flows discounted using a parallel-shifted swap curve.
- Incorrect bond terms can distort the projected cash flows and the resulting spread.
- Callable bonds may require option-adjusted spread when the embedded option materially affects value.
- The reference swap curve can materially affect short-maturity spread estimates.
- A eurobond is not necessarily denominated in euros.
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# Breaking out Swap curve + z-spread from a bond # Breaking out Swap curve + z-spread from a bond A colleague mentioned the following: She wanted to look at some bonds in Reuters/Bloomberg to see if they if they "correctly break-out the swap curve and z-spread". Would anyone understand what she is trying to say/do? Would be much appreciated ## Answer by Dimitri Vulis (score 3, accepted) https://quant.stackexchange.com/a/61579 OK I don't understand who "they" are supposed to be. Does "they" refer to Bloomberg/Refinitiv (your colleague is questioning whether Bloomberg/Refinitiv are right for this bond), or "they" refers to some other analytics, perhaps internal, that she wants to compare to Bloomberg/Refinitiv to see if they're in line? Generally, a Z-spread calculation is pretty straightforward: one has to project the cash flows of the bond and shift the swap curve up (in parallel) until the present value of the cash flows discounted with this shifted curve matches the observable (dirty) price of the bond. Things that can possibly go wrong with a Z-spread calculation include: - the bond's cash flows are not projected correctly because its indicative data is not set up correctly. For example, the bond might be amortizing, but the analytics don't know this and project cash flows as if it were a bullet bond. Or the coupon rate or the maturity etc might be wrong. (This happens on Bloomberg surprisingly often.) - the bond has some features that make Z-spread not the right calculation. For example, if the bond is callable and the call is not absurdly far from being at the money, then instead of Z-spread, you're better off looking at option adjusted spread (OAS). - The calculation uses a wrong swap curve. If the bond has less than 2 years to maturity, and you use swap curve built from swap rates for your Z-spread calculation, you'll get absurly low (possibly negative) Z-spread. This is the default setting on Bloomberg.You should change it to a swap curve built from futures instead. As an added bonus, note that "eurobonds" are not necessarily denominated in EUR.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.