Option Adjusted Spreads

What is Option Adjusted Spread?

Option-Adjusted Spread (OAS) is a yield spread which is added to the benchmark yield curve to price security with an embedded option. This spread measures the deviation of the security’s performance from the benchmark on the back of an embedded option. It is helpful in determining the price of complicated securities like mortgage-backed securities (MBS), collateralized debt obligationsCollateralized Debt ObligationsCollateralized debt obligation (CDO) refers to a finance product offered by the banks to the institutional investors. Such tranches have a complex structure and derive their value from the various underlying assets like loans, mortgages and corporate bonds, which also serve as collaterals in case of default.read more (CDO), convertible debentures, and option-embedded bonds.

The formula of Option Adjusted Spread

Spread differs from OAS only to the tune of options cost.

Option-Adjusted Spread(OAS) = Z-spread – Option Cost

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For eg:
Source: Option Adjusted Spreads (wallstreetmojo.com)

Example of Option Adjusted Spreads (OAS)

You can download this Option Adjusted Spreads Excel Template here – Option Adjusted Spreads Excel Template

Using a Monte Carlo simulation model, ten volatility paths are derived, and each path has a weight of 10%. The cash flows on each path are discounted by short-term interest rates plus a spread on that path. The present value of each path is mentioned below:

Present Value if the Spread is

Path70 bps75 bps80 bps85 bps

If the market price of the security is $79.2, what is the option-adjusted spread?

If the market price of the security is $75, calculate the option-adjusted spread?


The theoretical value of the security is the weighted average of the present value of all the paths. Since each path carries the same weight hence taking the simple average would provide the same results.

Present Value if the Spread is

Path70 bps75 bps80 bps85 bps
Sum of All (X)822792754729
No of paths (Y)10101010
Average PV (X/Y)

If the market price of the security is $ 79.2, then the corresponding OAS is 75 bps.

If the market price of the security is $ 75, then the option-adjusted spread is computed using linear interpolationInterpolationInterpolation is the mathematical procedure applied to derive value in between two points having a prescribed value. It approximates the value of a given function at a given set of discrete points. It can be applied in estimating varied concepts of cost, mathematics, statistics.read more.

Example 1-2

Difference in bps (between 2 available PVs)

  • = 75 – 80
  • = -5 bps

The difference in PVs (between 2 available bps)

  • = 75.4 – 72.9
  • = $ 2.5

Additional OAS (base 80 bps)

  • = -5 * (75.4-75) / 2.5
  • = -0.8 bps

OAS Spread when the price is $ 75

  • = 80 – (-0.8) bps
  • = 80.8 bps

Important Points about Option Adjusted Spread


  • Helps in the computation of the price of a security with an embedded option.
  • Reliable as the base calculation is similar to that of z-spread calculation.
  • Prepayment probability is based on historical data rather than an estimation.
  • Use of advanced models like Monte Carlo analysis in simulation.


  • Complex computation
  • Difficult to implement
  • Poor interpretation of OAS often results in a deformed view of the behavior of securities
  • Prone to model risk


Portfolio OAS is taken as the weighted average of the OAS of individual securities where weight is the market price of the securities. This limits the use of  OAS to such users who want to inspect the daily contribution to return at present. But to extend its relevance to a wide array of users, the spreads should be weighted by both durations and market weights.


Despite involving complex calculations and placing reliance on sophisticated models, the option-adjusted spread has turned out to be an analytical tool for the evaluation of embedded securities. An improvisation in the areas of limitation can increase its popularity and usage manifold.

Recommended Articles

This has been a guide to Option Adjusted Spreads. Here we discuss the formula to calculate Option Adjusted Spreads (OAS) along with examples,  advantages, and disadvantages. You can learn more about derivatives from the following articles –