Z-spread vs OAS

Nominal spread is the bond's YTM minus the yield of a same-maturity benchmark. Almost free to compute, which is why it survives. Its defects: it uses a single point on the curve rather than the whole curve, it assumes reinvestment at the bond's own yield, and (fatally here) it discounts the promised cash flows, which a callable will not pay.

G-spread repairs the first of those defects without touching the others. It is the bond's YTM minus the yield of a government bond interpolated to the bond's own maturity, rather than the yield of whichever benchmark happens to sit nearest. On a curve with a 3-year point at 4.70% and a 4-year at 4.90%, a note maturing in 3.5 years is referenced against 4.80%, not against either quoted point. The repair matters most exactly where careless quoting is most common: quoting the same note against the 4-year benchmark understates its spread by 10 bp and against the 3-year overstates it by 10 bp, and neither number is wrong about the bond, only about the reference.

How does the I-spread differ from the G-spread?

I-spread changes the reference asset rather than the interpolation. It is the bond's YTM minus the matched-maturity swap rate, interpolated the same way. Swaps quote continuously across maturities, they carry no idiosyncratic squeeze or scarcity of a particular government line, and they are the curve a dealer actually hedges on, which is why credit desks quote I-spreads and government desks quote G-spreads for the same bond.

The two differ by exactly one thing, and the identity is worth memorising:

G-spread − I-spread = the swap spread at that maturity

Work it once. A 3.5-year single-A note yields 5.55%. The interpolated government yield is 4.80% and the interpolated swap rate is 5.105%, a swap spread of 30.5 bp.

What happens to each spread in a flight to quality?

Now move the government leg and nothing else. A flight to quality takes the 3.5-year government yield down 20 bp to 4.60%, while the swap curve and the note's own yield stay where they are. The G-spread widens from 75.0 to 95.0 bp and the I-spread stays at 44.5 bp. Nothing about the issuer changed, nothing about the note changed, and a credit committee reading the G-spread has just been handed a 20 bp deterioration that exists entirely in the reference asset. The I-spread is not automatically the better number, because the swap curve carries its own bank-sector, collateral and regulatory drivers, which FI1.03's swap-spread section works through in detail. What it is, is a different number with different drivers, and the discipline is to name which reference you used before quoting a spread at all.

Both G and I are still single-point measures on the promised cash flows, so both inherit the remaining two defects: they read one point off the curve rather than the whole curve, and they discount cash flows a callable may never pay. The next two spreads fix those in turn.

What do the Z-spread and OAS each measure?

Z-spread (zero-volatility spread) is the constant spread added to every spot rate such that the promised cash flows discount to the market price. It fixes the curve-shape defect and not the option one: a Z-spread on a callable is computed on cash flows the bond may never pay.

OAS (option-adjusted spread) is the constant spread added to every rate in the calibrated tree such that the model value (with the exercise test switched on) equals the market price. Because exercise runs inside the valuation, OAS is a spread over the benchmark curve after the option has been paid for: what is left as compensation for credit and liquidity, and the only one of the three comparable across bonds with different option structures.

What is the option cost, and what sign does it have?

The bridge between them is the option cost:

Option cost (bp) = Z-spread (bp) − OAS (bp)

Its sign is a fact about ownership, and getting it right is a reliable marker of whether someone understands the framework:

• Callable → option cost is positive. The Z-spread flatters the bond because it ignores that the issuer can take it away. Strip that away and less spread remains. In this module's US example, Z = 74.70 bp, OAS = 56.20 bp, option cost = 18.50 bp.
• Putable → option cost is negative. The Z-spread understates the bond, because it ignores a right you own. On the Indian example (Worked Example 4), Z = 94.75 bp, OAS = 120.20 bp, option cost = −25.44 bp. Read as English: 25 basis points of the yield you appear to be giving up is actually the price you are paying for the put, and once you charge for it properly, the bond is compensating you 120 bp, not 95 bp.
• Option-free bond → OAS = Z-spread exactly. With no exercise test, the tree is just a two-dimensional way of discounting off the same curve. This is a useful sanity check on any implementation.

How do you use OAS for relative value?

The relative-value use. Two callables of similar credit quality and effective duration should trade at similar OAS; if X shows 82 bp and Y shows 61 bp, X is 21 bp cheap, conditional on both having been computed at the same volatility on the same curve. That conditional is not a footnote. Watch what the volatility assumption alone does to the same bond at the same price of 99.50:

Nothing about the bond or the market changed; the price is 99.50 in every row. Moving σ from 15% to 25% moves the OAS by 34 bp, more than the entire option cost. OAS is a model output, not a market observable, and the first question to ask about any OAS you did not compute yourself is "at what volatility?" Note the direction: higher σ makes the option more valuable, lowering the model's callable value at zero spread, so less spread is needed to reach the observed price, higher σ → lower OAS for a callable, and the reverse for a putable.