Z-Spread and Option-Adjusted SpreadOAS
The Z-spread is the constant spread that, added to the government spot-rate curve, makes a bond’s discounted cash flows equal its price. The option-adjusted spread goes further and uses a model to remove the effect of embedded options such as call rights.
A bond’s extra yield over government debt is its spread, but there are several ways to measure it. The simplest compares two yields. The Z-spread uses the whole government curve. The option-adjusted spread (OAS) also strips out the value of options inside the bond, such as an issuer’s right to call it or a homeowner’s right to prepay. This entry explains each measure and when to use it.
- Category
- Bonds and Interest Rates
- Reading time
- 4 min
- Also called
- Z-spread, Zero-volatility spread, Option-adjusted spread
- Updated
Z-spread and OAS in plain words
The Z-spread and OAS both work by discounting a bond’s cash flows at government rates plus a spread, and finding the spread that matches the market price.1 For a bond with no embedded options, the two are the same number.1
When a bond contains options, the OAS uses models to account for them. For mortgage-backed securities it is the most popular measure of value and risk premium.2 See Mortgage- and Asset-Backed Securities.
From simple spread to OAS, step by step
Nominal spread
Bond yield minus the yield of a government bond with similar maturity.
Use the whole curve
Discount each cash flow at its own government spot rate.
Solve for one spread
The constant spread that makes the present value equal the price is the Z-spread.
Model the options
Simulate many interest-rate paths and how the option behaves on each.2
Solve again
The spread that matches the price across all paths is the OAS.
Compare
Z-spread minus OAS shows roughly what the option costs the investor.
Worked examples
Example 1 — The nominal spread
Simple measureA corporate bond yields 5.20%. A government bond of similar maturity yields 4.00%.
| Nominal spread | 5.20% − 4.00% = 1.20% (120 basis points) |
Quick to compute, but it uses one point on the curve and ignores the timing of each cash flow.
Example 2 — Removing a call option
Option costA callable bond has a Z-spread of 180 basis points. A model values the issuer’s call right at 50 basis points of spread.
| OAS | 180 − 50 = 130 basis points |
Only 130 basis points is compensation for credit and liquidity; the rest pays for the option the investor sold. See Callable and Putable Bonds.
Example 3 — Comparing two bonds
Better comparisonBond A (no options) has an OAS of 90 basis points. Bond B (callable) has a Z-spread of 150 but an OAS of only 70.
| Looks cheaper by Z-spread | Bond B |
| Cheaper after options | Bond A |
OAS compares bonds with and without options on equal terms.
Nominal spread vs. Z-spread vs. OAS
| Aspect | Nominal spread | Z-spread | OAS |
|---|---|---|---|
| Benchmark | One government yield | Whole spot curve | Whole curve, many rate paths |
| Embedded options | Ignored | Ignored | Modelled |
| Model needed | No | No | Yes |
| Best for | Quick checks | Option-free bonds | Callable bonds and MBS |
Why these spreads matter
Relative value
Compare bonds of different structures fairly.
MBS valuation
OAS is the standard yardstick for agency MBS.2
Credit indices
Index spreads are often published as OAS. See Credit Spread.
Risk management
Spread changes drive returns on credit portfolios.
Advantages and disadvantages
Advantages
- Z-spread uses the full curve, not one yield.
- OAS allows fair comparison of bonds with options.
- Both are widely quoted by dealers and indices.
Disadvantages
- OAS depends on the model and its assumptions.
- Different models give different OAS values.
- Both measures break down for distressed bonds.
- Harder to compute than a simple yield spread.
Going deeper
Read as far as you need. Each level builds on the one before it.
What “spot curve” means
Beginner
A spot rate is the yield on a zero-coupon government bond for one maturity. The spot curve lists those rates across maturities. See Zero-Coupon Bond.
How OAS is computed for MBS
Intermediate
For mortgage securities, OAS calculations use Monte Carlo simulation with a calibrated interest-rate model and an estimated prepayment model.2 Prepayment assumptions therefore drive the result.
Where spreads stop working
Advanced
For deeply distressed issuers, spread measures can become misleading — bonds of different maturities may show wildly different spreads even though they default together — so markets switch to quoting prices.1 See Distressed Debt.
Common mistakes
Comparing Z-spreads of callable and non-callable bonds
Use OAS when options are involved.
Trusting one model’s OAS
Check the assumptions behind it.
Mixing benchmarks
Spreads over Treasuries and over swaps are not the same.
Using spreads for distressed bonds
Look at price and recovery instead.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Spreads measure a bond’s extra yield over government debt.
- The Z-spread uses the whole government spot curve.
- OAS also removes the value of embedded options.
- OAS is the standard measure for MBS and callable bonds.
- Both depend on assumptions and fail for distressed bonds.
Frequently asked questions
Why is OAS usually lower than the Z-spread for callable bonds?
Is OAS the same everywhere?
Which spread should beginners look at?
Further learning
- Credit Spread
The broader idea of spreads.
- Callable and Putable Bonds
The options OAS adjusts for.
- Mortgage- and Asset-Backed Securities
Where OAS is used most.
- Zero-Coupon Bond
The building block of the spot curve.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- Berd, Mashal and Wang (arXiv). Defining, Estimating and Using Credit Term Structures, Part 1 (opens in a new tab) Checked .
- Federal Reserve Bank of New York. Mortgage-Backed Securities (Staff Report No. 1001, 2022) (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.