## Introduction to Option Adjusted Spread

Option adjusted spread (OAS) is flat spread which has to be added to the treasury curve to make the theoretical price of an interest rate derivative equal to market price by using dynamic pricing models that take into account embedded options. This is the measure of spread over government treasury bond yields when all the options have been considered. It is applied in MBS, CDO, Convertible debentures and bonds with embedded options.

### Formula

It’s useful for option free bonds but not for a bond with an embedded option.

Option adjusted spread is used to measure the impact of optionality in the bond. It explicitly removes the value of an embedded option, giving spread for option free bond. It is defined as follows:

**Option Adjusted Spread = Z Spread – Option Cost**

For callable bond the issuer holds the right to buy back the bond at a call price (which is prespecified at the time of issue) if interest rates go down, market price of bond increases, the issuer has a right to redeem the bond at the call price which is less than the prevailing market price giving benefit to issuer. Option cost in this > 0 and hence OAS < Z.

For putable bonds, the option benefits the bond owner, it allows to sell back the bond at a higher price to the issuer if the interest rate goes up and the prevailing price goes down, hence Option cost is < 0 as OAS > Z.

### Example of Option Adjusted Spread

Let’s explain this by taking an example:

Suppose the market price of a bond is $102 and the price calculated using the treasury curve is $103.27. Now we choose a 60 basis point parallel shift in the treasury zero curves that give us the price of $101.20 which is less than the market price of $102. We need to decrease the Treasury zero curve to equate model price to market price of bond i.e. parallel shift will be somewhere between 0 and 60bp. A series of iterations is used to determine a parallel shift in the treasury curve that causes the model price to be equal to the market price.

Using linear interpolation, we get the below result:

On our second trial, we are using a 36.81 basis point that gives a bond price of $101.95 which is approximately equal to the market price of the bond.

OAS Spread will be slightly less than 36.81 calculated above.

### Type of Spreads

**Nominal Spread:**It is the difference between Yield to maturity of the risky bond and Yields to maturity of the risk-free bond (Treasury bond which is assumed to be risk-free). It is the rate added to the treasury par curve to get the market price of the bond or we can say the future stream of bond cash flows is discounted at the rate which is YTM. It is a poor measure as it ignores the term structure of the interest rate.**Zero volatility:**It spread (Z- Spread) is the single value-added to the treasury spot curve to give the discount rate that equates the present value of the bond to its current market price. This is done through a trial and error basis.

It is superior to nominal spread as it takes into the term structure of interest rate which is ignored in the earlier approach. Let’s denote the Present value of the risky bond as PV, Rf as the risk-free rate, z as the spread, C as the future stream of cash flows and FV is the future value of the bond which includes a coupon to be paid in future.

### Advantages of Option Adjusted Spread

Some of the advantages are:

- By separating bonds with an embedded option from its optionality feature investors can determine whether the investment is worthwhile or not.
- OAS provides a more accurate picture of embedded option contracts than just comparing the yield of two bonds. It uses advanced models like Monte Carlo analysis in simulation.
- Reliable as the calculation is similar to that of Z spread calculation. The OAS approach recognizes the security’s cash flows along each path, hence incorporate the optionality of cash flows into the analysis.

### Disadvantages of Option Adjusted Spread

Some of the disadvantages are:

- Measurement is complicated because OAS is very dynamic value, responding to changes in the level and shape of the yield curve, volatility, prepayments, credit spread, liquidity, etc.
- OAS is based on the assumption that historical data will be observed in the future.
- OAS model needs to be updated in case of any regime changes i.e. a shift in economic data in order to become responsive.
- Model dependent
- Difficulty in interpretation can result in the distorted picture of the behavior of securities

### Limitations of Option Adjusted Spread

Some of the Limitations are:

Portfolio OAS is usually calculated as a weighted average of OASs of component securities where weight is assigned based on the market price of securities. However, the greatest risk for an investor for embedded option bonds is a change in the interest rate and prepayment risk (which may lead to the early retirement of their investments before scheduled period) so weight assigned to the security should be a combination of duration and market price.

### Important Points to Remember

Some of the Important points are:

- For bonds with no embedded option OAS will be equal to Z spread.
- The difference between OAS and Z spread provides the implied cost of the embedded option
- OAS uses a number of scenarios carrying the possibility of numerous interest rate paths, different interest rate levels which are calibrated to the security yield curve to determine the cash flows along those paths and then the result is used in arriving the price of a security.
- For option embedded bonds volatility of an interest rate plays an important role to determine whether an option will be exercised or not.
- Two Mortgage-backed bonds with the same estimated maturity but with two different OAS Spread will provide different return i.e. bond with the higher OAS will be selling at a lower price as compared to bond with lower OAS and hence investor should consider earlier bond to maximize potential return.

### Conclusion

Despite involving complex calculations and dependence on sophisticated models, OAS has turned out to be an analytical tool and more superior to traditional methods for evaluating embedded securities.

### Recommended Articles

This is a guide to Option Adjusted Spread. Here we discuss formula and example of option-adjusted spread along with advantages, disadvantages, and limitations. You may also look at the following articles to learn more –

- Future vs Option
- Diluted Earnings Per Share
- Stock vs Options
- Personal Finance Basics
- Guide to Discount Rate Formula

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