Option-Adjusted Spread: How OAS Is Calculated

What Is Option-Adjusted Spread?

Option-adjusted spread (OAS) is the yield spread over the risk-free curve that a bond would offer if its embedded option were removed. It is the standard measure of compensation for credit and liquidity risk on bonds that carry embedded options, such as callable bonds, putable bonds, and mortgage-backed securities (MBS). The name comes from the adjustment: the spread is adjusted to strip out the value of the embedded option, leaving only the pure credit spread.

The problem OAS solves is that a callable bond's yield to maturity is not a clean measure of credit compensation. A callable bond pays a higher coupon than a comparable non-callable bond, but part of that extra yield is payment for the risk that the issuer calls the bond when rates fall. The OAS removes that option value so an analyst can compare the credit spread of a callable bond directly with that of a non-callable bond.

Why a Simple Spread Is Not Enough

The nominal spread, or G-spread, is the bond's yield to maturity minus the yield on a comparable-maturity Treasury. For a non-callable bond this is a reasonable measure of credit compensation. For a callable bond it overstates the credit spread, because the yield to maturity embeds the value of the call option the issuer holds.

The z-spread improves on the nominal spread by adding a constant spread to the entire Treasury spot curve rather than a single point on the yield curve. But the z-spread still ignores the embedded option. For a callable bond, the z-spread overstates the credit compensation by roughly the value of the call option. The OAS corrects for this by explicitly modeling the option and removing its value.

How OAS Is Calculated

OAS is computed with an interest rate model, typically Hull-White or Black-Derman-Toy, that simulates thousands of possible paths for future interest rates. The calculation proceeds in steps.

1. Build a model of the risk-free yield curve and the volatility of short rates.
2. Simulate many interest rate paths forward from today.
3. On each path, determine the bond's cash flows, applying the embedded option rules. For a callable bond, the issuer calls the bond when it is optimal, which happens when rates fall enough that refinancing is cheaper than paying the coupon.
4. Discount the cash flows on each path back to the present using the path's short rates plus a trial spread.
5. Average the present values across all paths.
6. Adjust the trial spread until the average present value equals the market price of the bond.

The spread that makes the model price equal the market price is the OAS.

Worked Example

Consider a callable bond priced at 101.00 with a 5% coupon and five years to maturity, callable at par in two years. The risk-free curve is flat at 3%. An analyst runs a binomial model with 10,000 paths.

On each path, the model checks whether the issuer calls the bond at the two-year call date. If rates have fallen so that the issuer can refinance below the 5% coupon, the bond is called and the cash flows stop at par. If rates have risen, the bond runs to maturity.

The model finds that a spread of 180 basis points over the risk-free curve makes the average discounted value equal the market price of 101.00. The OAS is therefore 180 bps.

Now compare the z-spread on the same bond. Because the z-spread ignores the call option, it treats the bond as if it always runs to maturity. The z-spread that prices the bond is higher, say 225 bps. The difference of 45 bps is the value of the call option. The OAS of 180 bps is the z-spread of 225 bps minus the option cost of 45 bps.

Measure	Value
Z-spread	225 bps
Option cost	45 bps
OAS	180 bps

The 45 bps gap is exactly the adjustment the OAS makes. It is the compensation the investor gives up because the issuer holds the right to call the bond.

Interpreting OAS

A wider OAS indicates more compensation for credit and liquidity risk after stripping out optionality. For a corporate callable bond, a widening OAS means the market is demanding more for the issuer's credit risk. For an MBS, the OAS reflects prepayment risk compensation, because homeowners can refinance when rates fall, which shortens the life of the security.

A negative OAS is possible and meaningful. Some agency MBS have traded at a negative OAS, meaning the market prices them rich relative to Treasuries on an option-adjusted basis. Investors accept a lower spread because of the perceived safety and liquidity of the securities.

Input Definitions

• Market price: The current price of the bond, used as the target the model must match.
• Coupon and maturity: The contractual cash flows of the bond, which the model discounts along each path.
• Call schedule: The dates and prices at which the issuer may call the bond. This defines the embedded option.
• Yield curve: The current risk-free spot curve, the baseline against which the spread is measured.
• Volatility: The assumed volatility of short rates. Higher volatility raises the value of the embedded option and lowers the OAS for a given price.

Important Caveats

Model Dependence

OAS is only as good as the interest rate model and the volatility assumption behind it. Two analysts using different models or different volatility inputs can derive different OAS values for the same bond. The measure is a modeling output, not an observed market price.

OAS Is Not a Trading Signal

A low or negative OAS does not by itself mean a bond is cheap or rich. It must be read against the issuer's credit quality, the liquidity of the issue, and the model assumptions. Comparing OAS across bonds is most meaningful when the same model and assumptions are used for all of them.

Prepayment Behavior Is an Assumption

For MBS, the OAS depends on an assumed prepayment model that predicts how quickly homeowners refinance as rates move. If actual prepayments differ from the assumption, the realized spread will differ from the modeled OAS.

Finance Information Disclaimer

This guide is provided for general informational and educational purposes only. It is not financial, investment, legal, or tax advice. Bond pricing and spread analysis require specialized models and judgment, and results vary with assumptions. Always consult a licensed financial adviser or investment professional before making investment decisions.

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