Z-Spread and OAS: Measuring Credit Spread Over the Curve

Key Takeaways

• The z-spread is the single constant spread added to every point on the benchmark spot-rate curve so that a bond's discounted cash flows equal its market price.
• The OAS is the z-spread with the value of any embedded option removed, isolating the pure credit and liquidity compensation.
• For a bond with no options the z-spread and OAS are equal; for a callable bond the OAS is lower, because part of the z-spread is really paying for the call risk.
• Use the z-spread to compare option-free bonds quickly, and use the OAS whenever the security has calls, puts, or prepayment behavior.

What It Is

The z-spread (zero-volatility spread) is the constant spread, in basis points, that you add to each spot rate on the Treasury or swap curve so the present value of a bond's cash flows matches its observed market price. Unlike a nominal spread, which compares a single yield to one point on the curve, the z-spread references the entire curve.

The option-adjusted spread takes the z-spread and subtracts the value of any embedded option, expressed in spread terms. It is computed through a model that simulates many interest-rate paths, values the option along each, and solves for the constant spread that reprices the bond once the option is accounted for.

Both are measured over a benchmark curve, and for both, a higher number means more compensation for risk.

The Intuition

A nominal spread quietly assumes the yield curve is flat. When the curve slopes, that assumption misprices every cash flow except the one it was measured against. The z-spread fixes this by discounting each coupon at its own maturity-matched spot rate plus the spread, so the shape of the curve is respected.

The z-spread still has a blind spot. If a bond can be called away, the investor is effectively short an option to the issuer, and some of the quoted spread is compensation for that risk rather than for credit. The OAS removes that piece, leaving a cleaner read on credit and liquidity. That is why OAS is the standard measure for callable corporates and mortgage-backed securities, whose cash flows shift with rates.

How It Works

Computing a z-spread is a search. You pick a spread, discount every cash flow at the matching spot rate plus that spread, sum the present values, and compare to the market price. If the total is too high, raise the spread; if too low, lower it. Iterate until the values match.

OAS adds a modeling layer. Because the option's value depends on future rate volatility, the calculation runs the cash flows through an interest-rate model (a binomial tree or Monte Carlo paths), values the option on each path, and finds the constant spread that reprices the bond given that option value. The relationship is:

• OAS = z-spread minus option cost (in spread terms).

For a callable bond the option belongs to the issuer, so the option cost is positive and the OAS sits below the z-spread. For a putable bond the option benefits the holder, so the OAS sits above the z-spread.

Worked Example

Take a 2-year bond with a 5% annual coupon and a face value of 100. The benchmark spot rates are 3.00% at 1 year and 3.50% at 2 years. The bond trades at 100.02.

Solve for the z-spread by adding a constant spread of 1.50% (150 bps) to each spot rate:

• Year 1: 5 / (1.0300 + 0.0150) = 5 / 1.0450 = 4.785
• Year 2: 105 / (1.0350 + 0.0150)^2 = 105 / (1.0500)^2 = 105 / 1.1025 = 95.238
• Present value = 4.785 + 95.238 = 100.02, which matches the market price.

So the z-spread is 150 bps. Now suppose the bond is callable and a rate model values that call option at 40 bps of spread. The option-adjusted spread is:

• OAS = 150 - 40 = 110 bps.

The bond looks like it pays 150 bps over the curve, but 40 of those basis points are simply rent for the call option the investor has written. Only 110 bps is genuine compensation for credit and liquidity. An investor who compared this bond's 150 bps z-spread to an option-free bond's 110 bps z-spread would wrongly judge the callable one as cheaper.

Common Mistakes

1. Comparing a z-spread to an OAS. They are on different scales for optioned bonds. Compare z-spread to z-spread and OAS to OAS, never across the two.
2. Using the z-spread for callable or mortgage bonds. For any security with an embedded option the z-spread overstates credit compensation. Reach for the OAS instead.
3. Ignoring the volatility assumption. OAS depends on the modeled rate volatility. A higher assumed volatility raises the option value and lowers the OAS, so two desks can quote different OAS numbers on the same bond.
4. Confusing the z-spread with a nominal spread. The nominal spread uses one curve point; the z-spread uses the whole curve. They match only when the curve is flat.
5. Forgetting the benchmark. A spread is meaningless without its curve. Quoting over Treasuries versus over swaps gives different numbers for the same bond.

Frequently Asked Questions

Q: What is the difference in z-spread vs oas in one sentence? The z-spread is the constant spread over the benchmark curve that reprices a bond, while the OAS is that same spread after the value of any embedded option has been stripped out.

Q: When does z-spread vs oas actually matter? It matters only for bonds with embedded options, such as callable corporates and mortgage-backed securities. For option-free bonds the z-spread and OAS are equal, so the choice is irrelevant.

Q: Is OAS always lower than the z-spread? No. For a callable bond the OAS is lower because the issuer holds the option. For a putable bond, where the holder owns the option, the OAS is higher than the z-spread.

Q: Why not just use the nominal spread? The nominal spread compares a single yield to one point on the curve and assumes the curve is flat. The z-spread respects the full shape of the curve by discounting each cash flow at its own maturity-matched rate.

Q: Does the OAS depend on assumptions? Yes. Because it requires valuing an option, the OAS depends on the interest-rate model and the assumed volatility. Change the volatility input and the OAS changes, which is why it is a model output rather than an observed market price.

Sources

1. Investopedia. "Z-Spread." https://www.investopedia.com/terms/z/zspread.asp
2. Investopedia. "Option-Adjusted Spread (OAS)." https://www.investopedia.com/terms/o/optionadjustedspread.asp
3. Investopedia. "Credit Spread." https://www.investopedia.com/terms/c/creditspread.asp
4. U.S. Department of the Treasury. "Daily Treasury Par Yield Curve Rates." https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.