What is the Options-Adjusted Spread? Definition, Formula, and Example
The options-adjusted spread is the yield spread over a risk-free benchmark that compensates investors for credit risk and embedded options in a bond.
What is the Options-Adjusted Spread?
The options-adjusted spread, or OAS, is the yield spread over a risk-free benchmark that a bond investor earns after stripping out the value of embedded options. It measures the compensation for credit risk, liquidity risk, and other non-option factors. The OAS is the most common way to compare bonds with callable, putable, or convertible features against plain-vanilla bonds.
The OAS answers a specific question: if a bond has an embedded option, how much extra yield does it offer relative to a risk-free bond after accounting for the option's value? A callable bond, for example, has a lower yield than a non-callable bond because the issuer holds the right to refinance. The OAS removes that option value to reveal the pure credit spread.
How the Options-Adjusted Spread is Calculated
The OAS calculation uses a binomial tree or Monte Carlo simulation to model interest rate paths. The process involves four steps:
1. Build an interest rate tree that models possible future short rates based on the current yield curve and volatility assumptions.
2. Price the bond with its embedded option along each path, using the tree to determine when the option would be exercised.
3. Find the spread that, when added to the risk-free rates in the tree, makes the theoretical bond price equal the market price.
4. Report that spread as the OAS.
The formula is:
Market Price = (1/N) × Σ [ Σ (Cash Flow_t / (1 + r_t + OAS)^t) ]
Where N is the number of simulated paths, r_t is the risk-free rate at time t, and OAS is the constant spread added to all risk-free rates. The OAS is the single number that makes the average discounted cash flow equal the market price.
Worked Example: OAS on a Callable AAPL Bond
Assume AAPL issues a 5-year callable bond with a 4% coupon, callable after 2 years at par. The bond trades at $101.50. The 5-year Treasury yield is 3.5%.
A standard yield-to-maturity calculation gives a yield of 3.75%, a spread of 25 basis points over Treasuries. But this spread understates the credit risk because the bond is callable. The issuer can refinance if rates fall, capping the bond's upside.
Using a binomial tree with 20% annual volatility, the option-adjusted spread calculation finds that the embedded call option is worth roughly 40 basis points of yield. The OAS is therefore:
OAS = 25 basis points + 40 basis points = 65 basis points
This means the bond offers 65 basis points of compensation for credit risk and liquidity, while the remaining 25 basis points of the nominal spread compensates the investor for the call option they sold to the issuer.
When Traders Use the Options-Adjusted Spread
Traders use the OAS to compare bonds across different issuers, sectors, and structures. A callable bond from AAPL with a 25 basis point nominal spread and a non-callable bond from MSFT with a 40 basis point nominal spread are not directly comparable. The OAS normalizes both for their embedded options, allowing a fair comparison of credit risk.
The OAS also serves as a valuation signal. When a bond's OAS widens, the market demands more compensation for credit risk, indicating deteriorating fundamentals or market stress. When the OAS narrows, credit conditions are improving. The OAS is the primary input for relative-value trades between corporate bonds, mortgage-backed securities, and asset-backed securities.
Limitations and Common Misconceptions
The OAS depends heavily on the volatility assumption used in the model. Higher volatility increases the value of embedded options, which lowers the OAS for a given market price. Two analysts using different volatility inputs will derive different OAS values for the same bond.
A common misconception is that the OAS equals the credit spread. It does not. The OAS removes the option value, but it still includes liquidity risk, prepayment risk, and other non-credit factors. The true credit spread is the OAS minus the liquidity premium, which is difficult to isolate.
The OAS also assumes the embedded option is exercised optimally, which is not always the case. Callable bond issuers may delay calling for non-economic reasons, and mortgage borrowers do not always prepay rationally. These behavioral deviations introduce model error.