Updated July 10, 2023

## Definition of Option Adjusted Spreads

Option-adjusted spreads measure the performance deviation of security by using the benchmark for embedded options. They add this mechanism to the benchmark yield curve to price the security.

Hence, they are also called the yield curve, which determines the valuation of complex securities such as mortgage-backed securities, collateral debt obligations, convertible debentures, and bonds with embedded options.

### Explanation

Option-adjusted spreads use the probability theory for the valuation of the bond spread. The “Yield-Curve spread” theory, which relies on a fixed cash flow model, opposes this theory. Implementing such a process entails complexity and demands substantial knowledge and technical expertise. Nevertheless, once achieved, this spread offers numerous long-term benefits.

### Purpose of Option Adjusted Spreads

- Many mechanisms use the benchmark yield curve for fixed cash flows. Investors use option-adjusted spreads for securities with embedded options because considering interest rate fluctuations is important.
- It is also used in the collateralized mortgage obligation market and the amortization class tranches. The securities which have the long-term form the highest portion of the option-adjusted spreads.
- Many other models, like the binomial model, use several assumptions. However, option-adjusted spreads are preferred for securities that do not possess such assumptions.

### Example of Option Adjusted Spreads

Mack wants to estimate the option-adjusted Spread of the seven years, 12% callable option with a face value of $2,000 and the present, the 189.6528 and the 10-year, 12% non-callable bond with a face value of $2,000, and a present value of 190.4589. Then, with the available figures, calculate a spread that can equate the prices of the two bonds.

**Solution:**

To calculate the spread, first convert the differences between the market price and the fair price of each bond into the yield.

Calculation of YTM is as below:

**YTM = ((Face value/Bond price) 1/Time period)-1**

- YTM of callable bond = ((2000 / 189.6528) 1/ 10)-1
- YTM of callable bond =
**5.456%**

Calculation of YTM of non-callable bond is as below:

- YTM of non-callable bond = ((2000 /190.4589) 1/ 10)-1
- YTM of non-callable bond =
**5.010%**

Calculation of Option-adjusted Spread is as below:

**Option-adjusted spread = YTM of callable bond – YTM of non-callable bond**

- Option-adjusted spread = 5.456% – 5.010%
- Option-adjusted spread =
**0.446%**

**Statement of calculation of Spread**

Particulars |
Value |

Face value of a callable bond | 2000 |

Face value of a non-callable bond | 2000 |

Present value of the present value of a callable bond | 189.653 |

Present value of a non-callable bond | 190.459 |

Time period | 10 |

YTM of a callable bond | 5.46% |

YTM of a non-callable bond | 5.01% |

Option-adjusted Spread | 0.45% |

Thus the option-adjusted Spread is 0.446%

### How to Determine OAS?

Below are the steps for the determination of the OAS:

- First, we calculate the discounted cash flows by using the prevailing interest rates of the particular securities.
- The sum of all the discounted cash flows is taken to calculate the theoretical value of the security. This theoretical value of the security also indicates the security’s market value.
- Many possible scenarios possess various interest rates; accordingly, the option-adjusted Spread is adjusted.
- In option-adjusted spreads, we consider various scenarios that carry several interest rate paths, and we add all of these paths to the security yield curve. Then, we determine the cash flows with all the paths and the security price.

### Advantages

- The option-adjusted Spread is considered reliable for the base calculation of other similar-natured security spreads.
- The prepayment’s estimation and probability do not depend on the estimation; rather than that, it depends on the past performance of the security or the historical data.
- In the simulation process of the option-adjusted spreads, Monte Carlo analysis and similar models are used. These are the most reliable models; hence, the option-adjusted spreads simulation process is considered reliable.
- The option-adjusted spreads help calculate and compute the security price with an embedded option.

### Disadvantages

- The Computation of the OAS is very complicated, and it is not that user-friendly. Therefore, one must possess good knowledge for such a complex computation and determination of the OAS.
- The implementation of the OAS is also very difficult to implement. These involve lots of technical and legal requirements, which take a lot of time.
- Sometimes, a wrong interpretation of the OAS can result in the wrong view of the security’s behavior.
- OAS is much more prone to model risk, and this risk sometimes results in negative trends in returns.

### Conclusion

Complex calculations and sophisticated models are involved in analyzing embedded securities, making the OAS an effective analytical tool. Improving the disadvantages of OAS can make these spreads more popular in the market, thereby increasing demand.

### Recommended Articles

This is a guide to Option Adjusted Spreads. Here we discuss the definition and example of option-adjusted Spread and its advantages and disadvantages. You may also look at the following articles to learn more –