- Sources of Return from Investing in a Bond
- How to Calculate Current Yield
- How to Calculate Yield to Maturity
- Bond Equivalent Yield Convention
- Yield to Maturity (YTM) Approximation Formula
- YTM and Reinvestment Risk
- Factors Affecting Reinvestment Risk
- Calculate Bond-Equivalent Yield of Annual-Pay Bonds
- How to Calculate Yield to Call of a Bond
- Cash Flow Yield
- Bootstrapping Spot Rate Curve (Zero Curve)
- How to Price a Bond Using Spot Rates (Zero Curve)
- Nominal Spread
- Z-Spread: Definition and Calculation
- Option-adjusted Spreads (OAS)
- What are Forward Rates?
- How to Calculate Forward Rates from Spot Rates?
- How to Value a Bond Using Forward Rates

# Option-adjusted Spreads (OAS)

The **Z-spread** handles one problem present in **nominal spread** effectively, i.e., that is, it measures the spread over the entire spot rate curve instead of only at one point in the curve. However, there is another problem that comes because of the embedded options. Due to the embedded options in the bonds, there is uncertainty about the future cash flows but both nominal spread and z-spread do not account for it. Option-adjusted spread is the third spread measure which takes care of this problem as well.

The option-adjusted spread removes the effect of embedded options on future returns, to reflect non-option risks when comparing a bond to a benchmark. It is the spread over the entire Treasury spot rate curve, but after accounting for the embedded options.

Unlike the other two spread measures, OAS reflects only credit and liquidity risk.

This is the best spread measure for comparing the yields of bonds with embedded options to Treasury yields.

The option-adjusted spread is model dependent and will vary based on the model used to compute it. It also depends on our assumption of the interest rate volatility. The higher the assumption of volatility, the lower will be the spread.

Below are a few points on how OAS compares to z-spread

- For bonds without options, OAS = Z-spread
- For a bond with call option, OAS is lesser than Z-spread
- For a bond with put option, OAS is great than Z-spread
- The difference between Z-spread and OAS is called
**Option cost**.

When the OAS for a bond is higher than the OAS of comparable bonds relative to the same benchmark, the bond is considered undervalued.

Alternatively, when the OAS for a bond is lower than the OAS of comparable bonds against their relevant benchmark, the bond is considered overvalued.

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